Free Printable Exponential Growth and Decay

1.

Which inequality best represents the domain of the part shown?

a)

$x>1$

b)

$y>1$

c)

$x>-2$

d)

$y>-2$

2.

A student used $f\left(x\right)=5.00\left(1.012\right)^x$ to show how the balance in a savings account will increase over time. What does the $5.00$ represent?

a)

The interest the savings account earned for the first year.

b)

The annual interest rate of the savings account.

c)

The number of years the savings account has earned interest.

d)

The starting balance of the savings account.

3.

Based on the table, which function represents the same relationship?

a)

$q\left(x\right)=\left(0.25\right)^x$

b)

$q\left(x\right)=256\left(0.25\right)^x$

c)

$q\left(x\right)=0.0625\left(4\right)^x$

d)

$q\left(x\right)=0.5\left(4\right)^x$

4.

What is the value of the y-intercept of the graph of $g\left(x\right)=73\left(\frac{4}{5}\right)^x$ ?

5.

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

a)

b)

c)

d)

6.

Which statement is the best interpretation of one of the values in this function?

a)

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

b)

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

c)

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

d)

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

7.

Scientists are studying a bacteria sample. The function $f\left(x\right)=245\left(1.12\right)^x$ gives the number of bacteria in the sample at the end of $x$ days. Which statement is the best interpretation of one of the values in this function?

a)

The initial number of bacteria is 12.

b)

The initial number of bacteria decreases at a rate of 88% each day.

c)

The number of bacteria increases at a rate of 12% each day.

d)

The number of bacteria at the end of one day is 245.

8.

There are 1,024 players in a tennis tournament. In each round, half of the players are eliminated. Which function can be used to find the number of players remaining in the tournament at the end of $x$ days?

a)

$f\left(x\right)=1,024\left(1.50\right)^x$

b)

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

c)

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

d)

$f\left(x\right)=1,024\left(0.05\right)^x$

9.

Which function models the total number of metric tons of copper produced in the year that is $x$ years since 1900?

a)

$c\left(x\right)=495,000\left(1.0325\right)^x$

b)

$c\left(x\right)=495,000\left(0.9675\right)^x$

c)

$c\left(x\right)=495,000x^{1.0325}$

d)

$c\left(x\right)=495,000x^{0.9675}$

10.

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?

a)

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

b)

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

c)

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

d)

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

11.

Which function models the amount of fertilizer in cubic yards left after $w$ weeks?

a)

$f\left(w\right)=0.97\left(78,000\right)^w$

b)

$f\left(w\right)=1.03\left(78,000\right)^w$

c)

$f\left(w\right)=78,000\left(0.97\right)^w$

d)

$f\left(w\right)=78,000\left(1.03\right)^w$

12.

The starting annual salary for an office worker at a company is $29,000. If the company awards an annual increase of 6.2%, which graph models this situation after the office worker receives $x$ annual increases?

a)

b)

c)

d)

13.

What is the graph of the function $f\left(x\right)=6\left(\frac{2}{3}\right)^x$ ?

Drag the two points and the asymptote to their correct positions.

14.

Scientists are studying a bacteria sample. The function $f\left(x\right)=245\left(1+0.12\right)^x$ gives the number of bacteria in thousands in the sample at the end of $x$ days.

Choose the correct answer from each drop-down menu to complete the statements.

The initial population of bacteria when the scientists began studying a bacteria sample was (a) .

The population is (b) at a rate of (c) each day.

Choose from the below words

245,000

increasing

12%

12,000

88%

112%

630,000

decreasing

Exponential Growth and Decay

Total questions: 14

Worksheet time: 11mins

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