REVIEW: Exponential Functions

1.

Multiple Choice

2 mins

1 pt

A particular type of cell doubles in number every hour. Which function can be used to find the number of cells present at the end of h hours if there are initially 4 of these cells?

$n=4\left(2\right)^h$

$n=4\left(\frac{1}{2}\right)^h$

$n=4+\left(2\right)^h$

$n=4+\left(\frac{1}{2}\right)^h$

2.

Multiple Choice

2 mins

1 pt

A student used $f\left(x\right)=500\left(1.012\right)^x$ to show how the balance in a savings account will increase over time. What does the 500 represent?

The interest the account earned for the first year

The annual interest rate of the savings account

The number of years the savings account has earned interest

The starting balance of the savings account

3.

Multiple Choice

2 mins

1 pt

Which statement about the graph $y=\frac{1}{3}\left(\frac{2}{3}\right)^x$ is true?

The graph has a VERTICAL asymptote

The graph crosses the y-axis at $\left(0,\frac{2}{9}\right)$

The graph has an asymptote at $y=\frac{1}{3}$

The graph decreases from left to right

4.

Multiple Choice

2 mins

1 pt

Scientists are studying the coronavirus very carefully. The function $f\left(x\right)=10000\left(1.05\right)^x$ gives the number of infected people in the world at the end of x weeks. Which of the following statements is the best description of one of the values in the function?

The initial number of infected people is 5

The number of infected people decreases at a rate of 95% each week

The number of infected people increases at a rate of 5% each week

The number of infected people at the end of 1 week is 10,000

5.

Multiple Choice

2 mins

1 pt

The graph of an exponential function is shown. Which of the following is NOT a true statement?

The domain is the set of all real numbers

The range is the set of all real numbers greater than 0

The equation of the asymptote is at $x=0$

The graph is decreasing from left to right

6.

Multiple Choice

2 mins

1 pt

There are 1,024 players in a Fortnite tournament. In each round, half the players are eliminated. Which function could be used to determine the number of players remaining at the end of x rounds?

$f\left(x\right)=1,024\left(1.05\right)^x$

$f\left(x\right)=1,024\left(0.95\right)^x$

$f\left(x\right)=1,024\left(-2\right)^x$

$f\left(x\right)=1,024\left(0.50\right)^x$

7.

Multiple Choice

2 mins

1 pt

Which graph best represents $f\left(x\right)=2\left(5\right)^x$ ?

8.

Multiple Choice

2 mins

1 pt

A bank account earning annual compound interest was opened, and no additional withdrawals or deposits were made after the initial deposit. The balance in the account after x years can be modeled by $b\left(x\right)=850\left(1.025\right)^x$ . Which statement is the best interpretation of one of the values in this function?

The initial balance in the account decreases at a rate of 97.5% each year.

The balance in the account increases at a rate of 2.5% each year.

The initial balance in the account was $1,025.

The balance in the account at the end of 1 year is $850.

9.

Multiple Choice

2 mins

1 pt

What is the value of the y-intercept of the graph of $h\left(x\right)=13\left(2.4\right)^x$ ?

2.4

40%

15.4

13

10.

Multiple Choice

2 mins

1 pt

The table represents some points on the graph of an exponential function. Which function represents the same relationship?

$f\left(x\right)=15\left(\frac{5}{6}\right)^x$

$f\left(x\right)=15\left(\frac{6}{5}\right)^x$

$f\left(x\right)=18\left(\frac{5}{6}\right)^x$

$f\left(x\right)=18\left(\frac{6}{5}\right)^x$

11.

Multiple Choice

2 mins

1 pt

Which graph best represents $f\left(x\right)=10\left(0.85\right)^x$ ?

12.

Multiple Choice

2 mins

1 pt

The graph of an exponential function is shown. Which dashed line represents the asymptote of the function?

Line A

Line B

Line C

Line D

13.

Multiple Choice

2 mins

1 pt

Five years ago, Vanessa bought a car for $25,000. Each year since then, the value of the car has decreased by 12%. Which of the following functions represents the value of Vanessa's car after x years?

$f\left(x\right)=25,000\left(1.12\right)^x$

$f\left(x\right)=25,000\left(0.88\right)^x$

$f\left(x\right)=25,000\left(0.12\right)^x$

$f\left(x\right)=25,000-12x$

14.

Multiple Choice

2 mins

1 pt

Five years ago, Vanessa bought a car for $25,000. Each year since then, the value of the car has decreased by 12%. What is the approximate value of the car after 5 years?

$44,000

$13,200

$650

$15,000

15.

Multiple Choice

2 mins

1 pt

The table contains some points on the graph of an exponential function. Based on the table, which function represents the same relationship?

$f(x)=0.04(0.2)^x$

$f(x)=(0.2)^x$

$f(x)=0.04(5)^x$

$f(x)=5(0.04)^x$

16.

Multiple Choice

2 mins

1 pt

Which statement about the graph of $y=12(0.4)^x$ is true?

The coordinates of the x-intercept are $\left(0.4,0\right)$

The equation of the asymptote is $x=0$

The graph includes the point $\left(4,0\right)$

The coordinates of the y-intercept are $\left(0,12\right)$

17.

Multiple Choice

2 mins

1 pt

Loany deposited $12,000 into an account that pays 2.50% interest compounded annually. If she makes no additional deposits, about how much money will she have in her account after 5 years?

$150,000

$13,600

$1,500

$10,600

18.

Multiple Choice

2 mins

1 pt

In 2013, Mr. Myers deposited $15,000 into a retirement account. Each year since 2013, the retirement account on average has increased by 7.5%. If this trend continues, about how much money will Mr. Myers have in his retirement account by 2035?

$74,000

$112,500

$20,000

$35,000

19.

Multiple Choice

2 mins

1 pt

In the year 2002, the total number of students in Austin ISD was 95,000 students. Each year since 2002, the total number of students in Austin ISD has decreased at an approximate rate of 2.75%. Which function represents the number of students in AISD after x years since 2002?

$s\left(x\right)=95,000x^{0.9725}$

$s\left(x\right)=95,000\left(0.0275\right)^x$

$s\left(x\right)=95,000\left(0.9725\right)^x$

$s\left(x\right)=95,000\left(1.0275\right)^x$

20.

Multiple Choice

2 mins

1 pt

Epidemiologists are studying the coronavirus COVID-19 in Italy. The function $f(x)=400(1.25)^x$ gives the number of people infected by the virus at the end of x weeks. Which statement is the best interpretation of one of the values in this function?

The number of people infected by the virus increases at a rate of 25% each week.

The number of people infected by the virus at the end of one week was 400.

The initial number of people infected by the virus decreases at a rate of 75% each week.

The initial number of people infected by the virus was 25.

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