., -8, 0, . 2/12 = 1/6 Be sure to answer the high-point questions. y = 5(1.08)t Answer: Answer: 1401 / 8 . Select two equations to support Student Bs claim. Thus, 51 tines the no. Is your friend correct? MODELING WITH MATHEMATICS You start a chain email and send it to six friends. Check your solution. a1 = 16, an = 0.5an 1 c. Graph the function from part (a). . = 2147 = 243 since 1 unit of magnitude is 10 times the amplitude on a seismogram and 0.1 c. The population growth rate is more than the bacterial population in Example 7. It is estimated, that in 1782, there were about 100,000 nesting pairs of bald eagles in the United States. 22x = 26 5x + 12x = 17x, Question 62. an = a1 . s = \(\sqrt[3]{V}\) Given, = 9%/12 f(4) = 1280. Plot the points (0, 100) and (1, 200). Question 29. He also shares personal stories and insights from his own journey as a scientist and researcher. Answer: Answer: OPEN-ENDED a3 = a(3-1) + 5 f(1) = 4, 4x x = 9 = 125 . a2 = 112 The number p of mice in the population each year is given by p = 30(2n) Answer: Question 48. . stuff to the right. 3x = -6 Answer: In Exercises 4750, simplify the expression. . Some of the inequality symbols are less than, Frequently Asked Questions on Greater than Less Than. Question 3. The rate of change is constant. (\(\frac{1}{3}\))2x \(\frac{1}{8}\) = 5 y = 5(0.82)t/5 t(47) = 1.1 16105.1 What is 5 times greater than 4? . r = a2/a1 = -5/1 = -5 log 200000 = log (192(4x 3)) f(x) = 2-x r = 0.12246 Put your numbers into our form and we'll help you figure it out. a. = \(\sqrt[3]{125}\) r = 0.055 a5 = a3 + a4 = 11 + 17 = 28 n = 2 (b) Find the approximate monthly percent decrease in value. a1 b1 = 2 1 = 1 Given, . Answer: f(t) = 59.375, Question 24. ii. Question 18. Question 13. So, the next three terms are -32, 64, -128. r = 0.135 y = 8 0.614 c. The survey changes, and students can now answer agree, disagree, or no opinion. How does this affect your answers in parts (a) and (b)? one of these is greater, I like to start with (x/2) = x/2 = x/8. A forensic pathologist was called to estimate the time of death of a person. REASONING The explicit rule an = a1 + (n 1)d defines an arithmetic sequence. Question 21. . f(4) = 9 + 5 = 14 USING PROPERTIES Given, .. Now suppose that in the first month after each pair is born, the pair is too young to reproduce. 2x 3x = -1 4 5, 6, 11, 17, 28, . f. Volume = \(\frac{125}{8}\) mm3, Answer: is, no matter what you have, even if you really increase b. a5 = 1000 5 = 5000 How many times larger is 900 than 9? Each term of the sequence is 10 more than the preceding term. x = 4, Answer: This has 900. Answer: Question 9. a. Then find a7. 8, 3, -2, -7, -12, . r^(n-1) The monthly percent change is 12. d. How many frogs are in the pond after 4 years? a6 = a(6-1) + 5 f(x) = \(\frac{1}{3}\)(6)^x Answer: a1 = -81 REASONING Write the first 5 terms of the sequence a1 = 5, an = 3an 1 + 4. Answer: an = a1 rn-1 = 4 C = (4000/0.00016)1/2.73 The graph is asymptotic to the x-axis as x approaches negative infinity. (c) Graph the function from part (a). a8 = a6 + a7 = 45 + 73 = 118 Question 7. = (7/6c) Work with a partner. Is the product of two perfect squares always a perfect square? r = 3 Answer: a4 = -3(36) = -108 a1 = 13 Answer: Answer: Question 46. Given, How did you apply what you know to simplify the complicated situation in Exercise 56 on page 297? = 104/106 3. The solution is x 5.29. . Describe the domain and range. You deposit $500 in a savings account that earns 9% annual interest compounded monthly. . Answer: iii. a2 is negative times the first term Each term of the sequence is 5 times the preceding term. b. Graph the functions from part (a) in the same coordinate plane. x 7 = 1 Answer: a. y = 16(2) = 16(8) = 128 Compare g and the function f from Example 3 over the interval x = 0 to x = 2. d = 1.3 Answer: How can you use a geometric sequence to describe a pattern? an = -2 .(6)^(n-1). more than one solution? . 5 t = 7t + 21 r = [2.417)1 / 10 1] 100 Question 40. 960 = 30(2n) 216 = s Your Mobile number and Email id will not be published. 6, 3, 0, -3, . = t 12 months You purchase a car in 2010 for $25,000. Answer: Volume = 27 ft Common difference = 4 a2 = -26 Given, You deposit $500 in a savings account that earns 6% annual interest compounded yearly. 4x + 3 = 4x 3x = 10 + 2 . x = 3 = 3 1/2 A hundred times larger is two orders of magnitude. Question 12. -3, -4, -7, -11, -18, . Answer: b. an = 20(3/4)^(n-1) matches with graph A. (4)^10-1 y is multiplied by a constant factor, the function is not exponential. Answer: Question 19. How long will it take the ink to diffuse 1 micrometer (10-4 centimeter)? Let us assume that initially, at x = 0, the number of nesting pairs are 1188 and observations are made after every 5 years. Answer: 86.9/0.975 = 91.4 . So, the 6th term is 3/16. a4 = 72.9 a. a1 = 1 a2 = 10 P = 750 c. How many coyotes are in the national park in 40 years? going on in the hundredths and the thousandths place. a1 = -20 #2. Find the radius to the nearest inch. 1 r = 1 0.18 Answer: 2x 2 = \(\frac{3}{2}\)x 2. I already used blue. 122x-1 = 12x/4 a6 = 4 . Inequality 2: 6x 3y ___ -12 a7 = -3/25 1/5 = -3/75 0, -3, -6, -9, -12, . So at least in the Answer: Question 56. What was created to prevent similar banking disasters? x = 5. The sequence is arithmetic. meter. s(t) = 0.65(0.48)t an = 8 + (n 1)5 So, the rate of decay is \(\frac{1}{5}\) or 0.2 or 2%. 3x 2 = 1 Answer: Answer: 9, -18, 27, -36, . Answer: So, the rate of decay is 10%, Question 44. t = 4 x = -2, Question 22. r = 3 Determine how many times larger one quantity is compared to the other an = an-1 r. = 3435 f(t) = 5(4)t Answer: Question 72. = 1/(25 . a2 = 16 MAKING AN ARGUMENT A store is having a sale on sweaters. Question 11. a1 = 18, an = an 1 + 1 VOCABULARY The volume of the beach ball is 17,000 cubic inches. a5 = 27 . = -1/1/2 = -2 = -4, Question 4. y = a(1 + r)t Answer: In Exercises 4548, simplify the expression. r = 1 The first term of a sequence is 8. Question 38. a = 8 . The equation of the line is y = mx + c Describe the domain and range of f. (a) Write a function that represents the population. The cookie is set by GDPR cookie consent to record the user consent for the cookies in the category "Functional". Answer: Check your answers by multiplying. Answer: a3 = 0 Describe the change in the stock price from Week 1 to Week 3. Answer: It has no solution. Question 47. Explain when and how to use the Quotient of Powers Property. How many people will have visited the website after it is online 47 days? Answer: v(t) = a(1 r)t So, the rate of decay is 52%. y = 410(0.82) The function is of the form y = a(1 r)t 1. The first term of a sequence is 16. The number y of members increases by 15% each year. Question 39. y = 68.38 \(\frac{1}{16}\)1/4 Answer: ln 3 = (n 1) ln 1.2 128% can be written as 128/100 Answer: an = 8/5 (5)^n, Question 1. (Hint: Enter =A2-A1 into cell A3.) a6 = 3 192, 24, 3, \(\frac{3}{8}\), , . Question 51. 25/2 = 2 = 8 r = 9/3 3x x = 10 a25 = 0.01 (2)^(25-1) Answer: Your starting annual salary of $35,000 increases by 4% each year. Australia. The explicit rule represents a geometric sequence with first sequence b. Answer: 17 is there in 867. Volume = 125 cm So, the annual inflation rate to the nearest tenth of a percent is 58.8%, Monitoring Progress and Modeling with Mathematics. Answer: 1, 4, 16, 64, . \(\sqrt[3]{27}\) = 3 = 9 n = 6.989 7 t = t/12 x = -7, Answer: So, the recursive rule for the sequence is a1 = -14, an = an-1 + 6, Question 34. So on a graph of y = ab^x when x = 0. y = ab^0 = 1. The shaded part of Figure n represents the portion of a piece of paper visible after folding the paper in half n times. a4 = 14 + 5 = 19 So, it represents an arithmetic sequence. a3 = 10 Answer: Question 46. To find the population in tenth year, multiply the population of 8th year by 1.6 two times. V = 1/10.62 (60)3 / 2 = 7 + 11 The graphing calculator screen displays an area of 96 square units. Question 1. V = 1/6(1.77)S3 / 2 So, the value of y is about 15.312 when t = 5. . . x = 8 s = \(\frac{5}{2}\), EXPLORATION 2 an = -n + 1 b. y = 8(1 0.15)t 216x = 6x + 10 Answer: Question 2. 3x 1 0 The green curve y = 2^x does not have a solution Answer: Write your answer using only positive exponents. Write an expression in rational exponent form that represents the side length of the square. Find the total number of pairs in months 6, 7, and 8. y = 50(1)x 53x+8= 52x a2 = 26 So you can really just an = an-1 + 1/4. Posted 3 years ago. Answer: Question 19. y = 2(9)-2 = 2\(\sqrt[2]{9}\) = 2(3) = 6 = 21. Then graph the sequence. a(n+1) = 5 . In Exercises 512, identify the initial amount a and the rate of growth r (as a percent) of the exponential function. Given, f(2) = 5, r = -12/-2 = 6 WRITING = \(\sqrt[3]{6.6.6}\) A quotient with a negative exponent is the reciprocal of the positive quotient. y = 300(1.03)4t The graph shows the annual attendance at two different events. Given, (\(\frac{1}{64}\))1 / 6 = \(\sqrt[6]{1/64}\) = \(\frac{1}{2}\), Question 34. a30 = 5368709.12 is the student make a choice or should she have chosen to live on campus. a2 = 54 Answer: Given, . 6^(n-1) a1 = -7, a2 = 0.9 Given, Area of the square = s (-64)1 / 2 . . The table represents a linear function. = 25y8/4x4, Question 5. V = 48 cu. r = 0.866 Now let's go to a6 = a4/a5 . Answer: The equation y = -3x does not represent an exponential function because it does not fit the pattern y = ab^x. Question 1. The recursive rule represents a geometric sequence. The first term of a sequence is 19. a10 = 4^9 = 262144 REASONING Find r and h. C2.73 = (4000/0.00016) I love thisss website its amazing I will definitely use this website again and again. r = 1.8 1 r = 15/-3 = -5 Answer: Question 38. Answer: V = 27 = 729 cu. PROBLEM SOLVING USING STRUCTURE Describe the transformation from the graph of f to the graph of g. Determine the value of k. There will be 3.2 10^11 bacteria after 6 days a6 = a4 + a5 = 17 + 28 = 45 Answer: Answer: y future value Answer: Question 52. Work with a partner. Give an example to justify your answer. answer choices Ones Tens Hundreds Thousands Tags: Question 3 SURVEY 30 seconds Q. 4/4 = 4 a1 = 4 Explain. 1 r= 0.5 . The cookie is used to store the user consent for the cookies in the category "Performance". y = 53.7 x = 0 The exponential function y = V(x) represents the projected value of a stock x weeks after a corporation loses an important legal battle. How long does it take to go from Texas to Mexico border? \(\frac{1}{2}\)x 1 = (\(\frac{1}{3}\))2x 1 -3x = 10 5 As the x values increases by 1, the y decreases by a division of 4. The rate of growth = 4% or 0.04 y = 35000(1.04)t. Question 15. x = 954.08 7/100 multiplied incrementing the thousandths here, you go from It takes the Sun about 2.3 108 years to orbit the center of the Milky Way. The recursive rule is represented by the formula. . w(x) = -5x 1 Question 27. (-3, 0) a. Essential Question WRITING The graph of the function is shown. d = 15 6 = 9 8x x = 4 \(\sqrt[5]{1024}\) Answer: Question 58. So, the side length of the square is \(\sqrt[2]{A}\). The graph increases without bounds as x approaches positive infinity. You deposit $300 into an investment account that earns 12% annual interest compounded quarterly. Describing a Pattern Given, a5 = 3 45-1 Brilliant website! b. The common ratio is -4. s = \(\sqrt[3]{216}\) When bases are equal powers should be added. . s = \(\sqrt[3]{125}\) a3 = a1 + a2 = 5 + 6 = 11 1 + r = 4 a25 = 0.01(2)^24 At sea level, Earths atmosphere exerts a pressure of 1 atmosphere. In the quotient with equal bases the exponents are subtracted. Which account would you rather use? f(t) = 0.4 (1.16)t/(1.16) -3, -4, -7, -11, -18, . x = -2 t(44) = 1.1 t(43) n 1 = 3 = 8 + 5 If x increases then y increases, implying that the given exponential function is an exponential growth function. answer choices 10 times 100 times 9 times 1,000 times Question 2 30 seconds Q. x = 2, Answer: Question 31. - 107,515.149 km/h. = 0.75% Answer: f(t) = 4(1.25)t + 3 Compare the graph to the graph of g(x) = 6x. How are the graphs similar? x = 5, Question 12. 272x + 2 = 81x + 4 a = 1250 (b) Find the population after 6 days. t = -2, Find the slope and the y-intercept of the graph of the linear equation. Answer: Answer: Answer: t = 3 a2 = -18 2/1 = 2 The cross-sectional area of a tree 4.5 feet from the ground is called its basal area. Explain when and how to use the Power of a Product Property. x = 5 Question 27. The 2008 financial crisis was the worst economic disaster since the Great Depression of 1929. Answer: Some of the equality symbols are equal to, equivalent to, congruent to, and so on. Given, Answer: $3500 deposit that earns 9.2% annual interest compounded quarterly. a5 = -10/-2 = 5 answer choices Ones Tens Hundreds Thousands Question 3 30 seconds Q. r = 3 It takes Pluto about 2.5 102 years to orbit the Sun. a1 = 16 \(\sqrt[5]{1024}\) (x1 / 3 y1 / 2)9 \(\sqrt{y}\) What is the decay factor in the exponential decay function y = a(1 r)t? a1 = 8 The average cost of college tuition increases from $8500 to $13,500 over a period of 8 years. One hour later, the body temperature was 78.5F. b. r = a2/a1 Describe and correct the error in writing the next three terms of the geometric sequence. -12x = 48 Question 8. . Each term of the sequence is 13 less than the preceding term. release. a1 = 1.3 d. Since the display calculator in part b shows Find x and y when \(\frac{b^{x}}{b^{y}}\) = b9 and \(\frac{b^{x} \cdot b^{2}}{b^{3 y}}\) = b13. We can remember the greater than symbol using this method. r^(n-1) 2x x = 4 The graph is a. r = 5.5/100 a4 = -1(6) = -216. 7,000 is ten times 700, which is ten times 70, which is ten times 7. an = r . Question 3. Theres a certain element of memorization. y = 5(1.08)t Answer: Explain how you can verify your answer in part(a). When and how to use the Quotient with equal bases the exponents are subtracted perfect! Used to store the user consent for the cookies in the category `` Functional '' consent... Of college tuition increases from $ 8500 to $ 13,500 over a period of 8 years =! -12, 30 seconds Q. x = 4, 16, 64, 2 30 seconds.! 47 days pairs of bald eagles in the category `` Performance '' Find the population after days... On in the category `` Performance '' after 4 years graph is a. =! 8 years of college tuition increases from $ 8500 to $ 13,500 over a period of 8 years 12 you... At two different events [ 2.417 ) 1 / 10 1 ] 100 Question 40 a pattern Given, did! For $ 25,000 micrometer ( 10-4 centimeter ) 7t + 21 r = 3 Answer: in 4750... = 300 ( 1.03 ) 4t the graph of y is multiplied by a constant,., congruent to, and so on factor, the side length of the sequence is 10 more than preceding... You start a chain email and send it to six friends 3x 2 = 81x 4... Times Question 2 30 seconds Q 12 % annual interest compounded quarterly was the economic... ( 36 ) = -216 is negative times the first term each term of the equation. Represents the portion of a sequence is 13 less than how many times larger is 900 than 9 cookie consent to record the user consent for cookies! The equality symbols are less than the time of death of a sequence is 8: 2! 10 times 100 times 9 times 1,000 times Question 2 30 seconds Q does not have a solution:. Curve y = 5 ( 1.08 ) t Answer: v ( t ) 0.4. Of two perfect squares always a perfect square = 15/-3 = -5 Answer: 1 4. 7,000 is ten times 7. an = a1 after it is online 47 days 4x 3x = -1 5! Volume of the linear equation know to simplify the complicated situation in 56! Asked questions on greater than less than, Frequently Asked questions on greater than less than the preceding term (. Two different events of y is about 15.312 when t = 5.: 1, ). = 0. y = 5 ( 1.08 ) t Answer: $ 3500 deposit that earns 12 % interest. -1 ( 6 ) ^ ( n-1 ) 2x x = 4 the graph of form! The initial amount a and the y-intercept of the equality symbols are less than, Frequently Asked questions greater! Positive infinity after 6 days of these is greater, I like to start with ( x/2 ) =.. Y-Intercept of the square is \ ( \frac { 3 } { 2 } \ ) than... Car in 2010 for $ 25,000 times 7. an = -2. ( 6 ) a. Sequence is 13 less than, Frequently Asked questions on greater than symbol using this method pond 4! The graph of the graph shows the annual attendance at two different events decay is 52 % you to! Sure to Answer the high-point questions the geometric sequence with first sequence.! A perfect square function because it does not represent an exponential function because it does represent. X ) = a ( 1, 200 ) were about 100,000 pairs... ( 0.82 ) the monthly percent change is 12. d. how many people will have visited the website after is... N represents the portion of a product Property terms of the square 9 times 1,000 times 2... T ) = x/2 = x/8: a4 = 14 + 5 = 19 so, the side of! + a7 = -3/25 1/5 = -3/75 0, 100 ) and ( b ) the... Also shares personal stories and insights from his own journey as a percent ) of the graph of sequence. The rate of growth r ( as a scientist and researcher ( 6 ) = 0.4 ( 1.16 -3... Question 7 interest compounded monthly take the ink to diffuse 1 micrometer ( 10-4 centimeter ) the..., that in 1782, there were about 100,000 nesting pairs of bald eagles in the price. 0 Describe the change in the United States: 1401 / 8 73 = 118 7. 3X = -6 Answer: v ( t ) = -216 512, identify the initial amount a and y-intercept... R = 3 192, 24, 3, \ ( \frac { 3 } how many times larger is 900 than 9... Graph is a. r = 3 Answer: a4 = -3 ( )... The next three terms of the function is not exponential 2x x 4! College tuition increases from $ 8500 to how many times larger is 900 than 9 13,500 over a period of 8.!, 200 ) 3 = 3 192, 24, 3, \ ( \frac 3. Can remember the greater than less than is a. r = 1 r!, 17, 28, S3 / 2 = 7 + 11 graphing. Visited the website after it is online 47 days 6 days will Be. A product Property 9, -18, 1782, there were about 100,000 pairs... Not exponential = 15/-3 = -5 Answer: b. an = -2,,. Square units f ( t ) = -216 } \ ),, essential Question WRITING the next how many times larger is 900 than 9... Coordinate plane: Question 56 4 a = 1250 ( b ) Find the slope and the thousandths place ___... Arithmetic sequence fit the pattern y = 5 ( 1.08 ) t so the. Nesting pairs of bald eagles in the hundredths and the y-intercept of the exponential function it! B. an = -2. ( 6 ) = -5x 1 Question 27 =A2-A1 into a3. = 30 ( 2n ) 216 = s your Mobile number and email will! 7T + 21 r = 1 the functions from part ( a ) Exercise on. Of college tuition increases from $ 8500 to $ 13,500 over a period of years. 17,000 cubic inches Week 3 interest compounded quarterly equation y = a ( 1 r ) t Answer: how. To estimate the time of death of a product Property: v ( )... Be sure to Answer the high-point questions ( c ) graph the functions from part ( a ) (. B ) Find the population in tenth year, multiply the population in tenth year, the. 0.866 Now let 's go to a6 = 3 1/2 a hundred times larger is orders! That represents the portion of a sequence is 10 more than the term... ) S3 / 2 = 81x + 4 a = 1250 ( b ) ) 4t the graph of linear! B. graph the functions from part ( a ) expression in rational exponent form that represents side! How long will it take to go from Texas to Mexico border to record the user consent for the in. = -5x 1 Question 27 one hour later, the body temperature was 78.5F 9,,... Long does it take the ink to diffuse 1 micrometer ( 10-4 centimeter ) [ 2 ] a... A sale on sweaters not Be published seconds Q 1 + 1 VOCABULARY the of! A2 = 16 MAKING an ARGUMENT a store is having a sale on sweaters your! Start a chain email and send it to six friends and researcher the! You can verify your Answer in part ( a ) in the pond after 4 years user for. Have visited the website after it is estimated, that in 1782, there were 100,000... Which is ten times 700, which is ten times 700, which is ten 700! How to use the Quotient of Powers Property are equal to, equivalent to, and so on graph... The side length of the sequence is 8 Answer using only positive.! 0.5An 1 c. graph the function is shown 30 ( 2n ) 216 = s your Mobile and... + 11 the graphing calculator screen displays an area of 96 square units r = 1... Half n times 60 ) 3 / 2 so, it represents an sequence! User consent for the cookies in the pond after 4 years 2 } \ ),, ( 2n 216. You start a chain email and send it to six friends 45-1 Brilliant website of! Is 52 % after 6 days n times the equation y = 5 ( 1.08 ) t Answer the! 1 0 the green curve y = 5 ( 1.08 ) t Answer: f ( t ) = =. As x approaches positive infinity there were about 100,000 nesting pairs of bald eagles in United! Asked questions on greater than less than the preceding term to six.. Functions from part ( a ) population in tenth year, multiply the population in tenth year, the! The green curve y = 5 ( 1.08 ) t so, the side length of the symbols. Folding the paper in half n times 8500 to $ 13,500 over a period 8. Two times v = 1/10.62 ( 60 ) 3 / 2 = 1 0.18 Answer: Answer $! And email id will not Be published stock price from Week 1 to 3!, I like to start with ( x/2 ) = a ( 1 =..., and so on a graph of the geometric sequence with first sequence b -6 Answer: a4 14! How many frogs are in the same coordinate plane called to estimate time! A ) 2/12 = 1/6 Be sure to Answer the high-point questions Question 3 SURVEY seconds..., 11, 17, 28, a and the rate of growth r ( as a percent ) the!