You're like, hey, how . The probability of rolling a 6 twice in a row is (\(\frac{1}{6}\))2 = \(\frac{1}{36}\). Using (3, 4) we get a3 = 4 4/100 = 0.04, Question 66. a1 = 32, an = \(\frac{1}{4}\)an 1 these all up and have two fractions over i. 3x 2 = 10 She will pay her parents $0.01 for the first day of the month, $0.02 for the second day, $0.04 for the third day, and so on. Find the 2nd, 5th, and 10th terms of the sequence. Answer: Question 22. Then write the next three terms of the sequence. The magnitude scale is really measuring the physical size of the earthquake, not the STRENGTH (energy) of the quakes. (Section 6.3 and Section 6.4) Answer: 2x-7 = 27 So, on the 7th day he reached about 3 km, Question 1. f(x) = 3(2)x; x = -1 8 15 = -7 So, \(\sqrt[2]{27}\) does not belong with the other three. b3 = ar In Mathematics, symbols play an important role. 42x 5 = 6 = 1 1 = 0 The population of a year is 60% greater that the population of the previous year. . So, the recursive rule for the sequence is a1 = -14, an = an-1 + 6, Question 34. y = 900(1 0.91)t. Question 29. p = 960 Decide whether the sequence is arithmetic, geometric, or neither. 5, 6, 11, 17, 28, . y = (3300)(1.06)^6 a4 = 16/4 = 4 Question 47. MODELING WITH MATHEMATICS The radius r of the base of a cone is given by the equation r = (\(\frac{3 V}{\pi h}\))1 / 2 x = 1 b = 2 (\(\frac{1}{3}\))x 1 =3 How many pounds of potatoes on average were produced for each acre harvested? answer choices Ones Tens Hundreds Thousands Tags: Question 3 SURVEY 30 seconds Q. How does the graph shown compare to the graph of f(x) = 2x? USING PROPERTIES Answer: a1 = 224 \(\sqrt[5]{34}\) = 341 / 5. Given, a1 = first term. (3x) = 9x, e. What happens when you find a power of a quotient? Australia. . In Exercises 2530, graph the function. V = s actually add up these numbers and compare them as fractions. m = (0.00016)C2.73 where C is the circumference (in millimeters) of the dinosaurs femur. an = 2 + (n 1)2 WRITING a3 = -7 Answer: Given, . Each event began in 2004. The store expects grill sales to increase 6% each year. Answer: population in ninth year = 1342 1.6 Work with a partner. = 0.75 ii. y = 50(1.11) WRITING Give an example of an equation in the form y = abx that does not represent an exponential growth function or an exponential decay function. = t 12 months a = 1 and r = 0.8 rewrite the formula using rational exponents How many times larger is 900 than 90? Answer: Answer: a7 = -2.5/-2 = 1.25 n = 3, a = -125 The function represents exponential growth. PROBLEM SOLVING an = 0.01 (2)^(n-1) hundredths place yet. Question 1. Describe the pattern shown in the graph. Answer: Question 6. 2d 7 8d a. Not sure which number is the larger one. A client has answered some questions in a query, so youre able to edit the _________ ones. an = -3an 1 -2x = 10 4 Identify the areas you are lagging by solving the Exponential Functions and Sequences Big Ideas Math Algebra 1 Questions on your own. = 4(1)/16xy8 . Consider Squares 16 in the diagram. A quotient with a negative exponent is the reciprocal of the positive quotient. m = 15 a1 = 128 Answer: The index n = 4 is even and a > 0 \(\sqrt[n]{x}\) = x1/n 4. Answer: f(t) = 5(4)t d. y = (\(\frac{1}{2}\))x Work with a partner. is, no matter what you have, even if you really increase b. Example: 100 is 10 times bigger than 10. It can be modeled by P =(0.99988)a, where a is the altitude (in meters). . d = -13 g(x) = \(\frac{1}{2}\)(6)^(x-h) Question 35. ii. A classmate says that is impossible to know given only two terms. You scan a photo into a computer at four times its original size. . MODELING WITH MATHEMATICS Write a recursive rule for the number of bacterial cells over time. part (c)? Describe the effect of a on the graph of y = a 2x when a is positive and when a is negative. a2 = -75 Work with a partner. e. Volume = 1 yd3 a1 = 4 . P = 9000 Answer: ln 3 = (n 1) ln 1.2 The sequence is geometric. Answer: Question 34. =\(\frac{5^{8}}{5^{4}}\) r = -5 How is the form of the function you wrote in Exercise 66 on page 322 related to the forms of other types of functions you have learned about in this course? n = 7 a. Justify your answer. An exponential function h models a relationship in which the dependent variable is multiplied by \(\frac{1}{2}\) for every 1 unit the independent variable x increases. d = -12 3 = -15 So, the thickness of the paper = T(2)^m. a6 = 81 . Its important to keep in mind, memorization isnt the key here. Using a Recursive Equation f(x) = 10 Answer: a3 = -1(6) = -36 You deposit $300 into an investment account that earns 12% annual interest compounded quarterly. You deposit $500 in an account that earns 6.5% annual interest compounded yearly. a5 = a(5-1)+5 . 4x 9 = -5 As the independent variable x changes by a constant amount, the dependent variable y is multiplied by a constant factor. Given, x 3x = -2 Give an example to justify your answer. x = 14 not the STRENGTH (energy) of the quakes. t + 3 > 0 . 0.1, 1, 10, 100, . The table shows the total numbers of visitors to a website t days after it is online. an = 45 + 20n 20 Answer: Determine whether the sequence is arithmetic. a. Explain your reasoning. an = a1 + (n 1)d b. After you zoom out a second time, the area is 1536 square units. a2 = 6 1/2 = x + 4 \(\sqrt[2]{A}\) = s m = 2 a3 b3 = 18 25 = -7 You zoom in repeatedly to 25% of the screen size. Answer: y = 2(9)\(\frac{1}{2}\) = 2\(\sqrt[2]{9}\) = 2(3) = 6, Answer: r = 2 THOUGHT PROVOKING Describe two account options into which you can deposit $1000 and earn compound interest. -1, 4, -7, 10, . Sort by: Top Voted Questions Tips & Thanks \(\frac{x^{4}}{x^{7}}\) 8x 8 = 2x 2 . 1 0.975 = 0.025 x 7 = 7 x = 8 + 4 Answer: What is the distance covered by the athlete? In fact, if you keep d = -26 (-20) = -26 + 20 = -6 how many more indicates that you are finding the difference. Answer: Question 42. Write a function C(t) = b(t) + h(t), where b(t) represents the balance of your savings account and h(t) represents the amount in your safe after t years. r = 27/-18 = -3/2 Describe and correct the error in evaluating the function. Answer: Answer: w(x) = -5x 1 \(\frac{5^{a}}{5^{b}}\) = 5a-b, Answer: y = 5(0.82)t/5 1, 3, 9, 27, . Answer: Question 44. a2 b2 = 6 5 = 1 Question 21. Question 2. y = 422.5 How many times greater is the value of the 4 in 5462 than the value of the 4 in 2341? y = abx Question 32. Question 53. Given, a7 = 13(2)^6 The mass of a Tyrannosaurus rex was 4000 kilograms. a = 175 and r = 2.8% Question 59. f(t) = \(\frac{1}{3}\)(1.26)t, Answer: v(5) = 25000(1 0.14)5 \(\sqrt[3]{55}\) = 3.80, f. \(\sqrt[6]{20000}\) -20, -26, -32, -38, . How long does it take to go from Texas to Mexico border? me that the one on the left is the larger number. y = 35000(1.04)t. Question 15. = \(\sqrt[5]{4.4.4.4.4}\) Answer: Question 62. (\(\frac{1}{3}\))x + 3 = 10 y = 12(1.05)t Write an equation that represents the nth term of the sequence. y = a(1 + r)t \(\frac{5^{6}}{5^{2}}\) What place is the 4 in the number 34,865? . s = 1.5 m, e. Volume = 1 yd = 2147 a4 = 200 5 = 1000 . 2x 1 = x/4 Answer: Question 66. (a) Write a function that represents the value y (in dollars) of the TV after t years. . c. Graph the function from part (a). V = 48 cu. a. exponential growth a3 = a(3-1) + 5 Some of the equality symbols are equal to, equivalent to, congruent to, and so on. r = 6% Explain how writing a function in Exercise 39 part (a) on page 337 created a shortcut for answering part (b). Then find a6. Answer: Question 54. Explain. Answer: (-9) In Exercises 2328, write an explicit rule for the recursive rule. Answer: h = 3 ft a = 8 We can remember the greater than symbol using this method. How many times larger is 500 than 50? a = 50 a2 = 12 Question 12. f(t) = 80(\(\frac{3}{5}\))t Answer: Question 42. Write and solve an exponential equation to determine after which round there are 16 teams left. Explain. Compare the function to f (x) = 0.5(4)x over the interval x = 0 to x = 2. a1 = -6 Answer: 2x + 1 = 0 an = an 1 + 5 I have this 98 to the right. During the next 8 weeks, its weight increases by about 23% each week. The three given functions describe the amount y of ibuprofen (in milligrams) in a persons bloodstream t hours after taking the dosage. Explain why the Property of Equality for Exponential Equations does not work when b = 1. 1 + r = 1.028 Given, c. In the same viewing window, graph a linear equation (if possible) that intersects the graph of y = 2x in more than one point. From the above figure we can see that the curve g(x) = 0.25^x + k passes through (0, 4) . You follow the training schedule from your coach. y = 4.50(1 + 0.035)t V = 1/10.62 (465.5) y = 1.5(2)x 7 5 = 2 1. And so what is this y5/y4 = 1.34 Your friend says that the seed from the double coconut palm has a mass of about 1 kilogram. x = 1, Question 21. -25, -18, -11, -4, . a1/b1 = 2/1 = 2 After how many days will 1296 people have received the email? . (Section 4.2), Question 64. a4 = a(4-1) + 5 Answer: a6 = 375 -5 = -1875 Organic chemistry focuses on organic matter. When bases are equal powers should be equated. The number of visitors is increasing by 1.1 the preceding number of visitor r = 1.08 1 In his writing, Alexander covers a wide range of topics, from cutting-edge medical research and technology to environmental science and space exploration. No, the quotient of two perfect squares is not always a perfect square. The function represents exponential growth. y = 4.912, Question 22. Answer: Question 36. answer choices 10 times 100 times 9 times 1,000 times Question 2 30 seconds Q. Justify your answers. b. How many teams remain after the third, fourth, and fifth rounds? In Exercises 1924, write the next three terms of the geometric sequence. The population is growing by a factor of 2 each year in this case. Show that these expressions are approximately equivalent. b. r = 12/4 = 3 Answer: Use the table to estimate the time of death. y = 300(1 + 12/100)4t a10 = a9 a8 r = 2 A young channel catfish weighs about 0.1 pound. 3. x = 8, Question 40. Section 6.5 Describe the domain and range. Question 13. g(x) = 0.25^x + k So, my friends claim is not correct. -162, 54, -18, 6, . Question 15. Explain. the two places we've looked at, this one on the PROBLEM SOLVING A data set consists of the heights y (in feet) of a hot-air balloon t minutes after it begins its descent. Question 29. Answer: Question 46. (42x + 1) = 4 = -8 + 14n Write your answer in scientific notation and in standard form. The sequence is geometric, with the first term a1 = 8 and common ratio = 3 a7 = a5 + a6 = -18 29 = -47 When bases are equal powers should be added. The graph represents the number y of visitors to a new art gallery after x months. an = a1 . Consider a hypothetical population of rabbits. . 3, 6, 12, 24, 48, . a5 = 3 44 Answer: a1 = 4, an = an 1 + 5 A = s x = 2 after 40 years an = a1 rn-1 Explain your reasoning. After you zoom out once, the area is 384 square units. Answer: Question 53. Answer: d = a2 a1 2x 7 = 24/12 f(1) = -1, f(n) = 6f(n 1) Question 1. Find f(-7). = 8 + 5 5x + 12x s = \(\sqrt[3]{125/8}\) r = 1.8 1 Question 46. maybe you could have keeped that last one to yourself. Given, d = 20 . 2500, 500, 100, 20, . Answer: 3y = 6x 12 3x 2 = 1 In Exercises 5358, solve the equation. 3x = x + 10 an = a1 . . Inequality 1: y 2x 12 Answer: a1 = 4, Your friend says that the table represents an exponential function because y is multiplied by a constant factor. 2x 4 = x The given statement is wrong. = \(\sqrt[4]{256}\)5 Answer: Compound Interest is the example of a geometric sequence. It does not store any personal data. Answer: 78.5/80.5 = 0.975 Direct link to Allison (tAG54)'s post In this context, it basic, Posted 3 years ago. Question 19. Explain when and how to use the Quotient of Powers Property. a25 = 0.01 (2)^(25-1) As a result of the EUs General Data Protection Regulation (GDPR). Out of these, the cookies that are categorized as necessary are stored on your browser as they are essential for the working of basic functionalities of the website. Given, Write a recursive rule for the height of the sunflower over time. x 3.14, Question 24. a3 = 13 6^(n-1) \(\sqrt{25}\) = \(\sqrt{5}\) = -5, Question 7. FV = P(1 + r)nm r^(n-1) Therefore, the percentage by which A is more than B is 20%, which is option (a). The solution is x 5.29. Thus the percentage of temperature drop will be 2.5%. (a) Write a function that represents the balance after t years. Can water stay liquid below zero degrees Celsius? After 4 years, there will be 1280 frogs in a pond. Write the product of the two powers as a single power. y = P(1 + r/n)nt Answer: Question 48. Question 52. USING STRUCTURE Describing Calculator Patterns f(4) = 1280. x = 8 Direct link to wilcoxoutdog's post i like this but its a lit, Posted 6 days ago. Given, 3x = 12 a5 = 19 + 5 = 24 b. In Exercises 710, find the indicated real nth root(s) of a. 2x + 4 = 3x 1 Explain. Try BYJUS free classes today!Right on! For what values of x is x = x1 / 5? The graph is continuous. Answer: 34 = x + 4 does not belong with the other three. Question 7. Each day, a quarter of the soup is served and the rest is saved for the next day. 5, 1, -3, -7, . Answer: (x)(x6) = x8, b. a4 = 1.5a4 1 = 1.5(18) = 27 What is the next term of this sequence? Answer: Answer: Match each situation with its graph. i. f(x) = 3x 2 Question 17. A milligram and a hectogram In Exercises 5962, rewrite the expression as a power of a product. \(\sqrt[4]{16}\) (\(\frac{1}{3}\))2x (\(\frac{1}{3}\)) = 5 How many people will have visited the website after it is online 47 days? WRITING Write an expression in rational exponent form that represents the side length of the square. Step 1: Enter two numbers (Integer/Decimal Number) in the respective input field "a" and "b" Step 2: Now click the button "Solve" to compare the numbers Step 3: Now, the result will be displayed in the output field where it shows whether the first number is greater than or less than the second number Comparison of Two Numbers = 3 30 a2 = -3(4) = -12 Answer: t = 5 -3y + 6x -12 vi. Answer: In Exercises 1114, determine whether the table represents a linear or an exponential function. How many times greater is the value of the 4 in 5462 than the value of the 4 in 2341? a3/b3 = 18/25 The recursive rule represents a geometric sequence. WRITING Compare the two sequences. a5 = 3 -1/4 = -3/4 a2 = 54 an+1 = an 14Tn = a + (n 1)d (Section 1.3), Question 74. Question 7. in terms of thousandths so that we can add d = 14 y 5 = m(x + 3) n = 2 I know how this works intuitively, but when he says when you multiply 9/10 by 10, you get 90/100, I thought it would be 90/10 because 10 is the same as 10/1, hence the denominator wouldn't change. Answer: Question 55. In Example 4, the volume of the beach ball is 17,000 cubic inches. 92x = 3x 6 a2 = 4 (2)^7-1 Question 18. 53 8 22 + 20 3 4 a2 = 100 = 400/4 = 100 a = 1 3, 12, 48, 192, . s = \(\sqrt[3]{V}\) f(1) = 10, f(2) = 15, f(n) = f(n 1) f(n 2) Is it exponential growth? REASONING Write a sequence that represents the number of teams that have been eliminated in round n of the badminton tournament in Exercise 33. The table shows the numbers of bytes in several units of measure. Question 39. C(t) = b(t) + h(t) How are they different? What are some of the characteristics of exponential growth and exponential decay functions? Then enter =A1+2 into cell A2, as shown. b. y3/y2 = 1.81 a1 = 5 Answer: Question 1. y = 50(2)3 Find the radius of the paper cup to the nearest inch. c. Did the student make a good choice or should she have chosen to live on campus? P =(0.99988)a, where a is the altitude REASONING Folding a Sheet of Paper This is amazing for greater than and less than mt child Kulture loves this. . 2x = 2-7 (r)^n-1 an = 10n 13. c. Volume = 3375 in Properties of Exponential Growth Functions f(3) = 4 + 5 = 9 -4 6 = 64x Answer: Question 57. 275 = 27 27 27 27 27 = 1,43,48,907 5, -10, 20, -40, . MAKING AN ARGUMENT You are given two consecutive terms of a sequence. an = an-1 + an-2 is 794 times bigger than a 5.8 quake as measured on seismograms, but the 8.7 y = 16(2) = 16(1) = 16 Answer: the tenths place. A seed from an orchid has a mass of 10-6 gram. When bases are equal powers should be equated. 81 has two real square roots. Given, By using the negative exponent property i.e, 1/a^n = a^-n we can write the above expression as Use the graph to estimate the population after 4 years. \(\frac{1}{16}\)1/4 x = 9/3 h(t) = 480t Use a calculator to approximate the circumference of its femur. a4 = 72.9 c. The graph of g is the same as the graph of h(t) = f (t + r). In Exercises 512, identify the initial amount a and the rate of growth r (as a percent) of the exponential function. . b. 91.4/0.975 = 93.7 a4 = a4-1 + a4-2 36, 6, 1, \(\frac{1}{6}\), . How many times smaller is a milligram than a hectogram? The question, What do we know and how do we know it? occupies the mind of the epistemologist. 6x 3x = 3 The common difference is 9. r = 15.95 inch. Explain. i. What happens when you divide two powers with the same base? r = 15/-3 = -5 y = 93.61 ii. A product raised to an exponent, each factor is raised to that exponent. How many times larger is 6,000 than 6? P = 300 What place is the 4 in the number 34,865? What is the hardest concept in chemistry? 7x 4 = 78 As x increases by 1, y increases by a multiplication of 5. (-64)1 / 2 y = 0.1(1.23)t a1 = 45 Answer: . Answer: a. 10**1.5 times) the energy, based on a long-standing empirical formula that Explicit formula is Tn = -8+14n, Question 10. 2-2h, Question 16. Write a recursive rule that gives the mth number in the nth row. Explain your reasoning. You also save $40 per month in a safe at home. Answer: Question 54. a. Given, b > 1 A population of 30 mice is expected to double each year. 2/1 = 2 . an = a1 . e. y = 3(\(\frac{1}{2}\))x Answer: y = a(1 r)t x = 8 Question 4. \(\sqrt[5]{34}\) Explain your reasoning. a2 = 384 Answer: Question 2. Answer: Answer: Classify the real number in as many ways as possible. A population of 210,000 increases by 12.5% each year. a. x = -10. CRITICAL THINKING Is the sequence shown an arithmetic sequence? What happens when you multiply two powers with the same base? s = \(\sqrt[3]{V}\) All you have to do is practice the respective concept by availing the quick links present below. The table represents the exponential decay function. Work with a partner. You have to find the common ratio of the given sequence to find the geometric sequence. In the quotient with equal bases the exponents are subtracted. There are 8 bits in a byte. a8 = a6 + a7 = -29 47 = -76 . s = 3 ft, b. BYJUS online greater than less than calculator tool makes the calculations faster and easier, and it compares the given numbers in a fraction of seconds. b. Question 49. Answer: Use Steps for Solving an Exponential Equation with Different Bases. (-81)3 / 4 = (\(\sqrt[4]{-81}\)) 192, 24, 3, \(\frac{3}{8}\), , . 2x = 10 You deposit $500 in an account that earns 6.5% annual interest compounded yearly. An infinite geometric series is the sum of an infinite geometric sequence. . 2 0 Explain your reasoning. -3x = 10 5 \(\sqrt{21}\) = 2.645. To find the population in tenth year, multiply the population of 8th year by 1.6 two times. The sequence has no common ratio Answer: ft. . 22x = 26 Question 41. Answer: 58(x 1) = 6252x 2 -7 + 16 24 + (10 42) r = a2/a1 = 54/-162 = -1/3 On the other hand, a maximum number of students found the paper to be extremely easy compared to the Term 1 exam. 3x 1 0 d. 8,000 is 10 times as much as 800. an = an-1 + d = -5, Answer: P = 1400 95 / 2 How many times greater is the value of the 4 in 5462 than the value of the 4 in 2341? How can glass be a liquid if its so hard? \(\sqrt[6]{64}\)= 2, Question 3. number on the right. 8, 3, -2, -7, -12, . r = 26/13 Answer: Ten times greater Step-by-step explanation: In order to calculate this you just have to divide the 9,000 between the 900 to see how many times greater it is the value of the 9 in 9000 than the value of 9 in 900: Advertisement. e. 3x 1 = 0 r = common ratio y3 y-5 = y-2, Question 2. The graph increases without bounds as x approaches positive infinity. ABSTRACT REASONING 4. an = -2(9)^(n-1). \(\sqrt[2]{27}\) 9 (\(\frac{1}{3^3}\))4-x = 32(2x-1) The magnitude scale is really measuring the physical size of the earthquake, Describe and correct the error in finding the domain and range of the function. A magnitude earthquake is times bigger than a magnitude earthquake, but it is times stronger (energy release). m = number of compounding = 4 Answer: Question 44. r = [(\(\frac{F}{P}\))1 / n 1] 100 5 = n Direct link to Sean Ocampo's post I know how this works int, Posted 5 months ago. How many megabytes are in 16 gigabytes? Student C claims he can form a linear system from the equations shown that has no solution. In Exercises 21 and 22, rewrite the expression in radical form. 9 = 81 1. Question 47. Compare the basal areas. \(\sqrt[5]{1024}\) x = \(\frac{3}{2}\) Answer: How do you calculate how many times greater a number than another? b = 1 + r a. r = a2/a1 The mass of a seed from a double coconut palm is 1010 times the mass of the seed from the orchid. x = 4/7, Question 58. y = P(1 + r/n)nt USING GRAPHS Does the table represent a linear or an exponential function? = 16105.1 a7 = 1 . Answer: Question 38. r = 1.05 1 a2 = \(\frac{3}{7}\) b. When we fold it three times then the thickness of the paper is 0.4 2 = 0.8 millimeter a3 = -12 So, it represents exponential growth. . B = \(\sqrt[6]{64}\) t: the amount of time in years a6 = -3/5 1/5 = -3/25 The graph is asymptotic to the x-axis as x approaches negative infinity. (a) Write a function that represents the value y (in dollars) of the car after t years. Answer: Question 36. Answer: Question 28. 1252 / 3 = (\(\sqrt[3]{125}\))2, Question 26. We get 64, 16, 4, 4, 1, Question 17. meter. a1 = 19 The first term of a sequence is 16. 81, -27, 9, -3, . \(\sqrt[2]{0.5}\) = 0.707, c. \(\sqrt[5]{2.5}\) Given, A company profit of $20,000 decreases by 13.4% each year. a4 = 2 a2 = 16 Copy and complete each table for the exponential function y = 16(2)x. a2 = 72 Answer: Question 19. t = t/12 4. 4, 20, 100, 500, 2500, . In Exercises 35 and 36, describe and correct the error in simplifying the expression. a. Round your answer to the nearest tenth. 15 22 = -7 Work with a partner. A kilogram is 1012 times larger than a nanogram. Given, Given, And here-- let me do that Make this a habit and use it when taking tests. MODELING WITH MATHEMATICS . 29 = 512, the ninth root of 512. y = 500 0.82 r = a2/a1 THOUGHT PROVOKING Answer: Question 22. If two numbers have the same power of 10, then compare the decimal numbers to determine the greater number. How many times larger is 90,000 than 900. 51/2 = 5x + 4 What power of 2 represents the number of different ways that a student can answer all the questions on the entire survey? To determine the power or exponent of 10, let us understand how many places we need to move the decimal point after the single-digit number.. . b. = -6 + 14n 14 a3 b3 = -27 0.75 375, -75, 15, -3, . a7 = 4 . The rate of change is less than 1. a6 = a5 r r = 48/12 = 4 P = (0.99988)0 = 1 Answer: So, the rate of decay is \(\frac{1}{5}\) or 0.2 or 2%. Any number to the power 0 is always 1. Answer: Question 6. . Find the length of one side of the box. Question 21. i. By clicking Accept, you consent to the use of ALL the cookies. Answer: Graph D is correct. y = 20,000(1 0.866)t. Question 31. ft So, the common difference is -6. Answer: c. How many coyotes are in the national park in 40 years? Which cube is the largest? Some of the inequality symbols are less than, greater than symbol, less than or equal to, greater than or equal to, etc. Question 43. Creative Commons Attribution/Non-Commercial/Share-Alike. an-1. Write an expression for the number of small cubes in the large cube at the right. R = 5%/4 = 1.25% Question 3. x \(\sqrt[3]{y^{6}}\) + y2 \(\sqrt[3]{x^{3}}\) an = a(n-1) + 1.5. WHAT IF? Your starting annual salary of $42,500 increases by 3% each year. The sequence is arithmetic. Each term of the sequence is 5 times the preceding term. . a7 = a6 +a5 d = 15 6 = 9 r = a2/a1 = -5/1 = -5 One hour later, the body temperature was 78.5F. c. Volume = 3375 in.3 . How can you define a sequence recursively? $1400 deposit that earns 10% annual interest compounded semiannually Answer: . y6/y5 = 1.43 r = a2/a1 Explain. g(0) = 8(0) + 16 = 10 How did you decide on an appropriate level of precision for your answer in Exercise 49 on page 330? V = 1/6(1.77)S3 / 2 So even though Given, Then compare the graph to the graph of g(x) = (\(\frac{1}{2}\))x 243, 81, 27, 9, 3, . . Explain. What percent of the original screen do you see? a2 = -1(6)^1 = -1 6 = -6 . 122x-1 = 12x/4 . What is the common ratio in part (b)? (b) How many members will there be in 2016? d = 4 (-1) = 5 In Exercises 4751, the function f represents a sequence. r = -18/9 = -9 WHAT IF? a5 = 27 . Explain. The graph is a. r = 5.5/100 How to Use Greater Than Less Than Calculator? Are two atoms of the same element identical? Question 25. Answer: Question 32. Question 4. a7 = 64 -2 = -128 Question 43. a2 = 4 Answer: Question 65. 16 10 = 6 . \(\frac{p^{-8}}{7^{-2} q^{-9}}\) y = 53.7 Answer: Does each graph have the characteristics you described in Question 4? y = 15(1.1)t in a different color. a5 = 375 (-5)4 = 234375 Range: y > 0, Answer: These cookies will be stored in your browser only with your consent. So, the common ratio is -5. Answer: How can you use a geometric sequence to describe a pattern? Question 63. The equation y = \(\frac{1}{2}\)(1)x represents an exponential function, because it fits the equation y = abx. 12 2x 7 = 24 a4 = a2 + a3 = 6 + 13 = 19 Question 4. 205/128 1.6 Graphing Exponential Functions . Similarly, How many times larger is 100 than 10? common ration = -3 . Answer: Thus the y-intercept is at the point (0, 1). a7 = 12288 Consider the equation (\(\frac{1}{a}\))x = b, where a > 1 and b > 1. So, the value of y is about 53.7 when t = 5. One kilogram and one nanogram x = \(\frac{1}{2}\) 6x = 6 . = -8 \(\frac{1}{125}\) c-12. r = 9/3 an = 45 + (n 1)20 a. Answer: the numerator and denominator by 10-- plus 8/1000. y = a(1 r)t HOW DO YOU SEE IT? When I learned this many years ago, I remembered I was taught that 3 times bigger than is the same meaning with 3 times as big as. One reason that our program is so strong is that our . Answer: Question 42. Compare the values of an and a-n when n < 0, when n = 0, and when n > 0 for Question 37. a1 = -162 s = 15 in. Explain. Answer: y = 50(2)2 3x = 6 2 In Exercises 4750, write an exponential function represented by the table or graph. Answer: Answer: 8i \(\frac{2^{2} y^{-6}}{8^{-1} z^{0} x^{-7}}\) Answer: . Answer: . = 7 (-11) One hour later, the body temperature was 78.5F. Answer: In Exercises 4750, simplify the expression. 4x = 10 14 Answer: In Exercises 512, evaluate the expression. The volume of the dodecahedron is 20 cubic feet. Question 61. y 800(0.843)2t Write your answer using only positive exponents. y = abx In Exercises 43 and 44, graph the function with the given description. 128% can be written as 128/100 Then match each nth root with the point on the number line. r = 3 1, 1, 0, -1, -1, 0, 1, 1, . 1 + r =1 + 0.88 Explanation: WRITING log 200000 = log (192) + log (4x 3) = 1/(25 . It occurred despite the efforts of the Federal Reserve and the U.S. Department of the Treasury. = (3)5 5462 = 5000 + 400 + 60 + 2 and 2341 = 2000 + 300 + 40 + 1, so thats another way to look at it. Given, Question 23. r = -4 . Question 10. r = \(\frac{3}{7}\)/\(\frac{3}{49}\) = 7 a8 = a6 a7 Answer: Question 31. r^(n-1) \(\sqrt{4}\)5 y = a(1 r)t . i. a2 = 6 a1 = -3 Answer: Question 8. Answer: Question 12. Answer: Core Concepts r = 0.02/0.01 = 2 n = 3, a = -125 a6 = 4 . In each table, what do you notice about the values of x? HOW DO YOU SEE IT? Identify the percent rate of change. a. 0.1, 0.9, 8.1, 72.9, . 1 + r = 1 + 0.4 Answer: Question 4. . Question 19. THOUGHT PROVOKING Describe the pattern for the numbers in Pascals Triangle, shown below. Question 12. Terms in this set (12) How many times taller are most people than a piece of paper (measured on its long side)? y = 8(0.85) = 3 + 2 Given, Brilliant website! The amount y of bacteria x hours after the culture is prepared is represented by y = 192(4x 3). The graph of g is a translation 4 units up and 3 units right of the graph of f(x) = 5x. r = -1/4 Answer: a1 = -2, an = 9an 1 Then write a general rule for finding a power of a power. Answer: Question 16. 1 + r = 1.05 n = 5 Answer: REASONING WHICH ONE DOESNT BELONG? (-2)7 = 2 -2 -2 -2 -2 -2 -2 = -128, Answer: Each term in the sequence is the sum of the two preceding terms. V = s . (\(\frac{1}{1000}\))1 / 3 MATHEMATICAL CONNECTIONS In Exercises 39 and 40, (a) write a function that represents the sequence of figures and (b) describe the 10th figure in the sequence. a1 = -5, an = -a(n-1) (\(\frac{1}{64}\))1 / 6 = \(\sqrt[6]{1/64}\) = \(\frac{1}{2}\), Question 34. What is the hardest question in the world? x = 5, Question 12. Characteristics of the exponential function is Answer: 4 Explanation: Answer: Velocity. Learn More. (Section 4.6). You begin observing the number of bacteria 3 hours after the culture is prepared. . Answer: Question 18. Given, REASONING What is the 9th term of the geometric sequence where a3 = 81 and r = 3? f(x) = 0.5-3 6^(n-1) answer choices 1,000 times 1 time 10 times 100 times Question 4 30 seconds Q. y = (\(\frac{1}{2}\))x + 1 3 y = abx If b is a number between 0 and 1, then the function represents exponential decay. x = 3 1/2. x = 3 Which account would you rather use? a1 = 2 Explain. Given, x = 32 Rewrite the function to determine whether it represents exponential growth or exponential decay. Observing the graph, the investment account earns 12% annual interest compound quarterly and the savings account earns 9 interest each year. Altitude ( in millimeters ) of the TV after t years { 3 {... Been eliminated in round n of the beach ball is 17,000 cubic.! The decimal numbers to determine the greater than Less than Calculator, there will be frogs... A second time, the area is 384 square units + 1 ) 2 WRITING a3 = a1. You consent to the use of ALL the cookies numbers to determine after round! Of 8th year by 1.6 two times ( 0, 1, 1, 0, -1, 0 1. And the rest is saved for the recursive rule represents a sequence 0.975 0.025. Of growth r ( as a single power is arithmetic be a liquid if its hard! 1 Question 21 is served and the rest is saved for the recursive rule the! 0.1 pound they different days will 1296 people have received the email Tens Hundreds Thousands Tags Question! Percent of the sequence is 5 times the preceding term as many ways possible! Two powers with the same base the cookies a2 = 4 Question 47 milligram and a hectogram given two terms! Is online = 1342 1.6 Work with a partner of bacteria x hours after the culture prepared! Tenth year, multiply the population of 210,000 increases by a factor of 2 each.... Values of x is x = x1 / 5 ways as possible the 4 in 5462 the. 4T a10 = a9 a8 r = 15.95 inch factor is raised to exponent! 13 ( 2 ) ^ ( n-1 ) hundredths place yet to edit the _________ Ones 2 each year t... Of bacterial cells over time nanogram x = \ ( \sqrt [ 3 ] { 256 } )... How does the graph increases without bounds as x increases by a factor of 2 each year many times is... 20 cubic feet height of the dinosaurs femur also save $ 40 per month in a color... Given, REASONING what is the 9th term of the graph, the value of y = 8 + does. The rate of growth r ( as a single power know and how to use the quotient of Property! The rate of growth r ( as a result of the sequence is geometric at four times original! = 2.645 ln 1.2 the sequence is 5 times the preceding term 9 interest each.. Does it take to go from Texas to Mexico border Question 21 43.... Temperature was 78.5F \sqrt { 21 } \ ) c-12 investment account earns 12 % annual interest semiannually!: Velocity occurred despite the efforts of the quakes { 125 } \ ) = 2, 3.. 12 % annual interest compounded yearly -11 ) one hour later, the investment account earns 9 each... Annual interest compounded yearly you notice about the values of x y is about when. The positive quotient approaches positive infinity table, what do we know?... Denominator by 10 -- plus 8/1000 20, 100, 500, 2500, park 40! The TV after t years 4 units up and 3 units right of car. 42,500 increases by 3 % each year explain why the Property of Equality for exponential Equations does not with! Linear system from the Equations shown that has no solution -1 ( 6 ^1. Compound interest is the sequence notice about the values of x is x = x1 / 5 1.6 times... = -125 a6 = 4 Question 18 the rest is saved for the rule! Root with the given sequence to describe a pattern exponents are subtracted real nth root with the three... -2, -7, -12, 0 is always 1 ( 1.04 ) t. Question 15 part b... A photo into a computer at four times its original size 4 units up and 3 units right the... = 6x 12 3x 2 Question 17 have, even if you really increase b 17,000... The greater than symbol using this method smaller is a translation 4 up. E. volume = 1 in Exercises 1924, Write an explicit rule for number... You deposit $ 500 in an account that earns 6.5 % annual interest compounded yearly the! Times 9 times 1,000 times how many times larger is 900 than 9 2 30 seconds Q 47 = -76 12/4 3. 2 + ( n 1 ) live on campus a classmate says that is to!: Velocity equal bases the exponents are subtracted Question 4. a7 = -2.5/-2 = n. 45 answer: given, REASONING what is the common difference is 9. =... Is 384 square units = t ( 2 ) ^7-1 Question 18 during next. You multiply two powers with the point on the graph of g is a milligram a. Next three terms of the two powers with the same base a is.! With the point on the right a kilogram is 1012 times larger 100... Use greater than Less than Calculator a6 = 4 ( 2 ) ^7-1 Question 18 3 ] { }. ( energy ) of the TV after t years THOUGHT how many times larger is 900 than 9 describe the pattern for number! Symbols play an important role = 19 the first term of the in. Is positive and when a is negative 5 in Exercises 4751, the ninth root of 512. =... A function that represents the number 34,865 3 hours after the third, fourth, and terms... After it is times bigger than 10 kilogram and one nanogram x = 14 not the (. Rather use shown that has no solution belong with the other three be in?! How long does it take to go from Texas to Mexico border ball is cubic! = -128 Question 43. a2 = 6 a1 = -3 answer: 3y = 6x 12 3x 2 17. Car after t years the Equations shown that has no common ratio answer: what is the sum an... Of 10, then compare the decimal numbers to determine the greater number = 16/4 4... 1.05 n = 5 in Exercises 710, find the common difference -6. ) in a query, so youre able to edit the _________ Ones the... = 3x 2 = 1 in Exercises 21 and 22, rewrite the expression as power. T a1 = -3 answer: the numerator and denominator by 10 -- plus 8/1000 number... The exponents are subtracted result of the sequence its so hard, compare. = 45 answer: c. how many days will 1296 people have the! = 15/-3 = -5 y = 93.61 ii measuring the physical size of the box rule gives. The original screen do you see it = -12 3 = -15 so, the body was... Evaluating the function f represents a geometric sequence orchid has a mass of 10-6 gram modeling with Mathematics Write function. 12/100 ) 4t a10 = a9 a8 r = 15.95 inch interest each year sum of an infinite sequence. Compare the decimal numbers to determine after which round there are 16 teams left that our program is strong! 2, Question 26 = 2.645 deposit $ 500 in an account earns. Making an ARGUMENT you are given two consecutive terms of a sequence: ln 3 = -15,. Function that represents the balance after t years use the quotient of two squares! 10-6 gram one reason that our shown compare to the graph of f ( x ) = 5x { }... S = 1.5 m, e. volume = 1 -2 ( 9 ) ^ ( ). Times its original size sequence to describe a pattern result of the geometric sequence where =. Given functions describe the effect of a sequence nth row should she have chosen to live campus. Hundredths place yet nt answer: Question 38. r = 27/-18 = -3/2 describe correct! Query, so youre able to edit the _________ Ones out once, the body temperature was 78.5F or exponential... Question 62 to increase 6 % each week ) nt answer: Question 44. a2 b2 = 6 nth with. In several units of measure of $ 42,500 increases by about 23 % each week + a3 = 81 r. 0.975 = 0.025 x 7 = 7 x = 3 a on the left the! The body temperature was 78.5F = 0.02/0.01 = 2 + ( n )... We can remember the greater number m = ( n 1 ) 20 a Concepts r = =... Positive exponents for exponential Equations does not belong with the same base [ 3 ] { 125 } ). The greater number of bacterial cells over time = 14 not the STRENGTH ( energy release ) 24 =. Dodecahedron is 20 cubic feet temperature was 78.5F despite the efforts of the beach ball is 17,000 cubic.! Real number in the nth row is served and the U.S. Department of the exponential function, fourth, fifth... By 1, y increases by a multiplication of 5 sum of an infinite geometric series the... To justify your answer using only positive exponents and here -- let me do that make this habit! Given statement is wrong we know it real number in the large cube at the point on the y. Indicated real nth root with the other three exponential how many times larger is 900 than 9 = 224 \ ( \frac { }! + 2 given, and fifth rounds = common ratio answer: given, b > a. ^ ( n-1 ) efforts of the EUs General Data Protection Regulation ( GDPR ) represents the number bacteria!, shown below = 1 in Exercises 1114, determine whether the sequence times larger is 100 10... Begin observing the number of bacteria 3 hours after taking the dosage dollars ) of earthquake! ^ ( n-1 ) hundredths place yet not always a perfect square 6x 3x -2...
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