Quiz about Algebra 1 - Ch. 6.4 Exponential Growth & Decay Pg. 327-328

Question 1

Problem #26

Write a function that represents the situation.

A company profit of $20,000 decreases by 13.4% each year.

Accepted Answer

$$y=20,000\left(0.866\right)^t$$

Answer

$$y=20,000\left(0.686\right)^t$$

Answer

$$y=2,000\left(0.866\right)^t$$

Answer

$$y=20,000\left(0.68\right)^t$$

Question 2

Problem #28

ERROR ANALYSIS: You purchase a car in 2020 for $25,000. The value of the car decreases by 14% annually. Describe the error in finding the value of the car in 2025.

Accepted Answer

The decay rate is 1 - 0.14, not 1 + 0.14.

Answer

The decay rate is 1 - 14, not 1 + 14.

Question 3

Problem #28

ERROR ANALYSIS: You purchase a car in 2020 for $25,000. The value of the car decreases by 14% annually. Correct the error in finding the value of the car in 2025.

Accepted Answer

$$v\left(t\right)=25,000\left(0.86\right)^5$$ $$\approx11,761$$

Answer

$$v\left(t\right)=25,000\left(0.86\right)^5$$

$$\approx14,761$$

Answer

$$v\left(t\right)=25,000\left(1.14\right)^5$$ $$\approx48,135$$

Question 4

Problem #28

ERROR ANALYSIS: You purchase a car in 2020 for $25,000. The value of the car decreases by 14% annually. Describe and correct the error in finding the value of the car in 2025.

What is the value of the car in 2025?

Accepted Answer

The value of the car in 2025 is about $12,000.

Answer

The value of the car in 2025 is about $15,000.

Answer

The value of the car in 2025 is about $17,000.

Answer

The value of the car in 2025 is about $10,000.

Question 5

Problem #32

Determine whether the table represents an exponential growth function, an exponential decay function, or neither.

Accepted Answer

exponential growth function

Answer

exponential decay function

Answer

neither

Question 6

Problem #32

Determine whether the table represents an exponential growth function, an exponential decay function, or neither. Explain.

Accepted Answer

As x increases by 1, y is multiplied by 3.

Answer

As x increases by 2, y is multiplied by $$\frac{1}{6}.$$

Answer

As x increases by 1, y is divided by 2.

Question 7

Problem #34

Determine whether the table represents an exponential growth function, an exponential decay function, or neither.

Accepted Answer

exponential decay function

Answer

exponential growth function

Answer

neither

Question 8

Problem #34

Determine whether the table represents an exponential growth function, an exponential decay function, or neither. Explain.

Accepted Answer

As x increases by 2, y is multiplied by $$\frac{1}{6}.$$

Answer

As x decreases by 2, y is multiplied by $$\frac{1}{6}.$$

Answer

As x increases by 1, y is multiplied by 3.

Question 9

Problem #38

Determine whether the function represents an exponential growth or exponential decay.

Accepted Answer

exponential

growth

Answer

exponential

decay

Question 10

Problem #38

Determine whether the function represents an exponential growth or exponential decay.

Identify the percent rate of change.

Accepted Answer

8%

Answer

19%

Answer

18%

Answer

1.8%

Question 11

Problem #44

Determine whether it represents exponential growth or exponential decay.

Accepted Answer

exponential

growth

Answer

exponential

decay

Question 12

Problem #44

Rewrite the function to determine whether it represents exponential growth or exponential decay.

Accepted Answer

$$y\approx14.8\left(1.4\right)^t$$

Answer

$$y\approx14.8\left(0.4\right)^t$$

Question 13

Problem #50

Determine whether it represents exponential growth or exponential decay.

Accepted Answer

exponential

decay

Answer

exponential

growth

Question 14

Problem #50

Rewrite the function to determine whether it represents exponential growth or exponential decay.

Accepted Answer

$$r\left(t\right)\approx\left(0.60\right)^t$$

Answer

$$r\left(t\right)\approx\left(1.60\right)^t$$

Question 15

Problem #58 a

MODELING REAL LIFE: Your checking account has a constant balance of $500. Let the function m represent the balance of your savings account after t years. The table shows the total balance of the accounts over time.

a. Write a function B that represents the total balance after t years.

Accepted Answer

$$B\left(t\right)=2000\left(1.02\right)^t+500$$

Answer

$$B\left(t\right)=200\left(1.02\right)^t+500$$

Answer

$$B\left(t\right)=2000\left(1.02\right)^t+50$$

Answer

$$B\left(t\right)=2000\left(1.2\right)^t+500$$

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