Free Printable Unit 5 Exponential Functions Review

1.

Which graph represent the exponential decay of a radioactive element?

a)

A

b)

B

c)

C

d)

D

2.

Which of the following is an exponential function?

a)

$y=3x^2$

b)

$y=3x-1$

c)

$y=3^{\left(x-1\right)}$

d)

$y=\frac{x-2}{3-x}$

3.

Identify all the tables that are exponential functions.

a)

b)

c)

d)

4.

$y=4^x$ The graph of this equation is shifted three units to the left and one unit up. What is the new equation?

a)

$y=4^{\left(x+1\right)}-3$

b)

$y=4^{\left(x+3\right)}-1$

c)

$y=4^{\left(x-3\right)}+1$

d)

$y=4^{\left(x+3\right)}+1$

5.

Which of the following equations could represent the graph?

a)

$y=3^x+2$

b)

$y=3^x-2$

c)

$y=3^{\left(x+2\right)}$

d)

$y=3^{\left(x-2\right)}$

6.

In recent years, the number of students who participate in cheerleading has decreased. The function

y=24,200\left(0.986\right)^x

where y is thousands, and x is the number of years since 2005, models the number of people who are on their high school cheerleading team. Estimate the number of students who are on their high school cheerleading team in 2012. Round your answer to the nearest whole number.

(a)

7.

Jennifer bought a tractor that depreciates at a rate of 7% per year. The tractor costs $52,000. Which equation represents the value of the tractor after 8 years?

a)

$y=52000\left(0.93\right)^8$

b)

$y=52000\left(0.07\right)^8$

c)

$y=52000\left(1.93\right)^8$

d)

$y=52000\left(1.07\right)^8$

8.

Which equation represents an exponential decay?

a)

$y=5.2^x$

b)

$y=\left(\frac{5}{2}\right)^x$

c)

$y=0.52^x$

d)

$y=5\cdot2^x$

9.

A radioactive substance decays at a rate of 6% per year. If the initial amount of the substance is 150 grams, which of the following functions models the remaining amount of the substance, in grams, after t years?

a)

$f\left(t\right)=150\left(1.06\right)^t$

b)

$f\left(t\right)=150\left(0.94\right)^t$

c)

$f\left(t\right)=150-150\left(1.06\right)^t$

d)

$f\left(t\right)=150-150\left(0.94\right)^t$

10.

A colony of rabbits has a population of about 18,000 bunnies and is growing at a rate of about 1%. A colony of bees has a function describing its population as: $b\left(t\right)=12000\left(1.02\right)^t$ . Which animal population has the higher growth rate?

a)

Rabbits

b)

Bees

11.

Jose bought a house for $140,000. Each year it appreciates at a rate of 2.5%. What will the total value of the house be at the end of the 8th year? Round to the nearest hundredth place.

(a)

12.

The price of a new washing machine is $1020. If the value of the washing machine decreases 4% per year, what will be the price of the washing machine after 5 years? Round to the nearest hundredth place.

(a)

13.

If a population of flies starts with 62,000 flies and dies at a rate of 24% each year. Which of the following represents the situation?

a)

$y=24\left(62,000\right)^x$

b)

$y=62,000\left(0.24\right)^x$

c)

$y=62,000\left(1.24\right)^x$

d)

$y=62,000\left(0.76\right)^x$

14.

Ashley invested $125 into an account that has 2.75% annual interest rate. What equation best describes this investment after t years?

a)

$y=125\left(0.0275\right)^t$

b)

$y=125\left(1.275\right)^t$

c)

$y=125\left(1.0275\right)^t$

d)

$y=125\left(0.0925\right)^t$

15.

A used car was purchased in July 2006 for $15,900. If the car depreciates 13% of its value each year, what is the value of the car, to the nearest whole dollar, in July 2014?

(a)

16.

Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Which equation represents this situation?

a)

$y=5000\left(0.7\right)^x$

b)

$y=5000\left(1.3\right)^x$

c)

$y=30\left(5000\right)^x$

d)

$y=5000\left(x\right)^x$

17.

Michael invested $5000 into an account that has a 5.5% interest rate that is compounded quarterly. What equation best describes this investment after t years?

a)

$y=5000\left(1+0.055\right)^t$

b)

$y=5000\left(1+\frac{0.055}{12}\right)^{12t}$

c)

$y=5000\left(1+\frac{0.055}{2}\right)^{2t}$

d)

$y=5000\left(1+\frac{.055}{4}\right)^{4t}$

18.

The half-life of carbon-14 is approximately 6000 years. If we have 800 grams of this substance, how much of it will remain after 30,000 years?

(a)

Unit 5 Exponential Functions Review

Total questions: 18

Worksheet time: 42mins

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