Module 10: Interpreting Inputs and Outputs for Exponential Functions Quiz

Step 1 of 1

Flynn invested $30,000 into a mutual fund, which earned an average of 9.2% each year for the past 10 years. If this trend continues, the amount of money, in dollars, in Flynn's account can be modeled by this exponential expression:

A(t)=30,0001.092tA(t)=30,0001.092t,

wheretis the number of years since Flynn invested the money. Examine the following graph depicting this situation.

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Question 1 of 13

Question1

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Estimate when the amount of money in the account will double.

The amount of money in the account will double after approximately 8years.

The amount of money in the account will double after approximately 6years.

The amount of money in the account will double after approximately 9.5years.

The amount of money in the account will double after approximately12.5years.

Kavoxand Nadir have been successfully lowering the cost of labor since their businesses started. The cost of labor at both companies, in percentage of revenues, can be modeled by two exponential functions:

N(t)=240.98tN(t)=240.98tandK(t)=320.96tK(t)=320.96t

wheretis the number of years since 2000.These functions are depicted in the following GeoGebra applet.

[The graph shows two exponential functions, for Kavox and Nadir, comparing number of years since 2000 on the x-axis versus labor cost as percentage of revenue on the y-axis. Both functions generally increase from left to right. Point A open parenthesis 6.18 comma 11.24 close parenthesis is marked on Nadir's curve and point B open parenthesis 9.48 comma 12.04 close parenthesis is marked on Kavox's curve. Moving both points to y = 16 results in open parenthesis 20.06 comma 16 close parenthesis for A, Nadir, and open parenthesis 16.98 comma 16 close parenthesis for B, Kavox.]

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Question 2 of 13

Question2

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Which company decreased its labor cost to16%earlier? How many years before its competitor did it reach this standard?

Kavoxdecreased its labor costto16%approximately4.7years earlier than Nadir.

Kavoxdecreased its labor costto16%approximately1.58years earlier than Nadir.

Kavoxdecreased its labor costto16%approximately3.09years earlier than Nadir.

Nadir decreased its labor costto16%approximately3.09years earlier thanKavox.

Cameron saved $1,000in an account which pays2%annual interest. The amount of money, in dollars, can be modeled by the functionf(x)=1,0001.02xf(x)=1,0001.02x,wherexstands for the number of years since the investment was made. The function is depicted in the following graph.

[A graph plots Number of Years on the x axis and Amount of Money in Dollars on the y axis. A curve begins at approximately (0, 1120) and slopes gently upward through (28, 1800).]2018 WGU, Powered by GeoGebra

Question 3 of 13

Question3

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Estimate the function's valuewhenx= 20.

In function notation, the estimated valueisf(1480)$20f(1480)$20.

In function notation, the estimated valueisf(20)$38,340f(20)$38,340.

In function notation, the estimated valueisf(20)$1,200f(20)$1,200.

In function notation, the estimated valueisf(20)$1,480f(20)$1,480.

Use the following applet to solve the next problem.

[The graph shows two functions, one linear and one exponential, for Yummy (linear) and Amigo (exponential), comparing number of months since January 2015 on the x-axis versus number of customers on the y-axis. Both functions generally increase from left to right. Point A on the Yummy linear function open parenthesis 8.87 comma 2274.55 close parenthesis and point B on the Amigo exponential function open parenthesis 19.24 comma 7314.7 close parenthesis are marked. Moving both points to y = 5000 results in A = open parenthesis 22.5 comma 5000 close parenthesis and B = open parenthesis 17.53 comma 5000 close parenthesis.]

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Question 4 of 13

Question4

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How many months before Yummy Chinese did Amigo reach5,000customers?

Actually, Yummy Chinese reached5,000customers earlier than Amigo.

Amigo reached5,000customers approximately6months before Yummy Chinese.

Amigo reached5,000customers approximately10months before Yummy Chinese.

Amigo reached5,000customers approximately5months before Yummy Chinese did.

Kavoxand Nadir have been successfully lowering the cost of labor since their businesses started. The cost of labor at both companies, in percentage of revenues, can be modeled by two exponential functions:

N(t)=240.98tN(t)=240.98tandK(t)=320.96tK(t)=320.96t,

wheretis the number of years since 2000.These functions are depicted in the following GeoGebra applet.

[The graph shows two exponential functions, for Kavox and Nadir, comparing number of years since 2000 on the x-axis versus labor cost as percentage of revenue on the y-axis. Both functions generally increase from left to right. Point A open parenthesis 6.18 comma 11.24 close parenthesis is marked on Nadir's curve and point B open parenthesis 9.48 comma 12.04 close parenthesis is marked on Kavox's curve. Moving both points to y = 20 results in open parenthesis 9.02 comma 20 close parenthesis for A, Nadir, and open parenthesis 11.51 comma 20 close parenthesis for B, Kavox.]

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Question 5 of 13

Question5

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Using the applet,determinewhich company decreased its labor cost to20%earlier.How many years before its competitor did it reach this standard?

Nadir decreased its labor costto20%approximately4.87years earlier thanKavox.

Kavoxdecreased its labor costto20%approximately2.49years earlier than Nadir.

Nadir decreased its labor costto20%approximately1.21years earlier thanKavox.

Nadir decreased its labor costto20%approximately2.49years earlier thanKavox.

Cameron saved$1,000in an account which pays2%annual interest. The amount of money, in dollars, can be modeled by the functionf(x)=1,0001.02xf(x)=1,0001.02x,wherexstands for the number of years since the investment was made.The function is depicted in the following graph.

[A graph plots Number of Years on the x axis and Amount of Money in Dollars on the y axis. A curve begins at approximately (0, 1120) and slopes gently upward through (28, 1800).]2018 WGU, Powered by GeoGebra

Question 6 of 13

Question6

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Estimate the function's value wheny= 2,200.

The function's value is2,200whenx15.5x15.5.

The function's value is2,200whenx35x35.

The function's value is2,200whenx42x42.

The function's value is2,200whenx39.8x39.8.

Due to technology advancement and competition, hard disk price per gigabyte (GB) has been decreasing exponentially.Penbleand Quexoare competing hard disk manufacturers. The price of hard disk, per GB, at those two companies can be modeled by the functions in the following graph, where the red solid function represents the hard disk price of Quexo, and the black dotted line represents the hard disk price of Penble.

[The graph shows two exponential functions, p of x and q of x.Thefunctions compare time since 2000 on the x-axis to the price per gigabyte ofhard disks for two companies,Penble and Quexo. The price per gigabyte of Penble's hard drives is given by p of x. The price per gigabyte of Quexo's hard drives is given by q of x.Below are some coordinates for p of x.(3.6, 1.50),(4, 1.40),(10, 0.56),(11, 0.50).Below are some coordinates for q ofx.(3,1.50),(4, 1.30),(9.6, 0.50),(10, 0.46). ] 2018 WGU, Powered by GeoGebra

Question 7 of 13

Question7

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Estimate the price difference in 2004. (Remember,tis the number of years since 2000.)

Quexo'shard disk was approximately$0.20more expensive per GB thanPenble's.

Penble'shard disk was approximately$0.10more expensive per GB thanQuexo's.

Penble'shard disk was approximately$0.70more expensive per GB thanQuexo's.

Quexo'shard disk was approximately$0.10more expensive per GB thanPenble's.

Flynn invested $30,000 into a mutual fund, which earned an average of 9.2% each year for the past 10 years. If this trend continues, the amount of money, in dollars, in Flynn's account can be modeled by this exponential expression:

A(t)=30,0001.092tA(t)=30,0001.092t,

wheretis the number of years since Flynn invested the money. Examine the following graph depicting this situation.

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Question 8 of 13

Question8

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Estimate the amount of money in the account after six years.

The amount of money in the account after 6 years will be approximately $36,000.

The amount of money in the account after 6 years will be approximately $120,000.

The amount of money in the account after 6 years will be approximately $80,000.

The amount of money in the account after 6 years will be approximately $51,000.

When a certain virus attacks a PC, it drains the CPU's computing power. The following function models the CPU's available computing power, in percentage, since the virus attack:

f(x)=100(0.8)xf(x)=100(0.8)x,

wherexstands for the number of minutes passed since the attack started.

The function is depicted in the following graph.

[A graph plots Minutes since Attack on the x axis and Available CPU Power in Percentage on the y axis. A curve begins at (0, 100) and falls with decreasing steepness toward the x axis through (20, 0).]

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Question 9 of 13

Question9

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Estimate the function'sx-valuewheny= 60.

The function's value is60whenx2.3x2.3.

The function's value is60whenx12.6x12.6.

The function's value is60whenx4x4.

The function's value is60whenx1.8x1.8.

Question 10 of 13

Question10

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The number of memberships at Yoga Fitness can be modeled by the function,C(x)=50,00020.2xC(x)=50,00020.2x,wherexis the number of years since 2010.

Predict the number of customers Yoga Fitness will have in 2020.

The company will have200,000customers in 2020.

The company will have no customers left in 2020.

The company will have12,500customers in 2020.

The company will have about534,275customers in 2020.

Gloriaworks for the United Nations. Her team was tasked with predicting the world's populationin the near future. Many important policy and business decisions will be made based on this prediction. The team used exponential regression as the very first step in their prediction. (They expect to add more factors later to fine-tunethe results.) World population landmark data is provided in the following table.

Years Since 1900	World Population in Billions
27	2
59	3
74	4
87	5
99	6
111	7

The following appletmodelsdata in the table by using an exponential function.

[The graph shows a scatterplot and an exponential function fit to the data. The graph compares number of years since 1900 on the x-axis versus world population in billions on the y-axis. The function generally increases from left to right. The points are located at open parenthesis 27 comma 2 close parenthesis, open parenthesis 59 comma 3 close parenthesis, open parenthesis 74 comma 4 close parenthesis, open parenthesis 87 comma 5 close parenthesis, open parenthesis 99 comma 6 close parenthesis, open parenthesis 111 comma 7 close parenthesis, and open parenthesis 119.03 comma 8 close parenthesis. Point open parenthesis 119.03 comma 8 close parenthesis is designated as point A. The r-value is 0.98. Moving point A to y = 5.5 results in open parenthesis 94.68 comma 5.5 close parenthesis.]

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Question 11 of 13

Question11

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Based on the data, what will the world's population be in 2050?

By thepoint(150,13.9), you can see that the world's population will be13.9billion in 2050.

By thepoint(150,12.87), you can see that the world's population will be12.87billion in 2050.

By thepoint(150,11.92), you can see that the world's population will be11.92billion in 2050.

By thepoint(50,2.77), you can see that the world's population will be2.77billion in 2050.

Kavoxand Nadir have been successfully lowering the cost of labor since their businesses started. The cost of labor at both companies, in percentage of revenues, can be modeled by two exponential functions:

N(t)=240.98tN(t)=240.98tandK(t)=320.96tK(t)=320.96t,

wheretis the number of years since 2000.These functions are depicted in the following GeoGebra applet.

[The graph shows two exponential functions, for Kavox and Nadir, comparing number of years since 2000 on the x-axis versus labor cost as percentage of revenue on the y-axis. Both functions generally increase from left to right. Point A open parenthesis 6.18 comma 11.24 close parenthesis is marked on Nadir's curve and point B open parenthesis 9.48 comma 12.04 close parenthesis is marked on Kavox's curve. Moving both points to x = 7 results in open parenthesis 7 comma 20.84 close parenthesis for A, Nadir, and open parenthesis 7 comma 24.05 close parenthesis for B, Kavox.]

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Question 12 of 13

Question12

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In 2007, what was the difference, in percentage of revenue, of labor cost atKavoxand Nadir?

In 2007,Kavox'slabor cost was3.21%morethan Nadir's.

In 2007, Nadir's labor cost was3.21%more thanKavox's.

In 2007,Kavox'slabor cost was2.66%more than Nadir's.

In 2007,Kavox'slabor cost was3.79%more than Nadir's.

Flynn invested $30,000 into a mutual fund, which earned an average of 9.2% each year for the past 10 years. If this trend continues, the amount of money, in dollars, in Flynn's account can be modeled by this exponential expression:

A(t)=30,0001.092tA(t)=30,0001.092t,

wheretis the number of years since Flynn invested the money. Examine the following graph depicting this situation.

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Question 13 of 13

Question13

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Estimate how long it will takefor the amount ofmoney to increase from $40,000to $50,000.

It will take approximately 3.9yearsfor the amount ofmoney to increase from $40,000 to $50,000.

It will take approximately 7.9yearsfor the amount ofmoney to increase from $40,000 to $50,000.

It will take approximately 3.3yearsfor the amount ofmoney to increase from $40,000 to $50,000.

It will take approximately 2.6 years for the amount of money to increase from $40,000 to $50,000

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