Free Practice Quiz Question List

03 Exponential Functions Online Quiz Questions

Use this free practice quiz with 20 questions to review 03 Exponential Functions, test your knowledge, and prepare for your next test or exam.

20 questions

Choose one

1 point

A quantity is modeled by $Q(t)=Q_0(0.72)^t$ . What does the factor 0.72 represent?

A
The quantity grows by 72% each interval.
B
The quantity retains 72% of its previous value each interval.
C
The quantity decreases by 72 units each interval.
D
The quantity changes by a constant amount of 0.72.

Choose all

1 point

Which two statements correctly describe the function $f(x)=ab^x$ when $a>0$ and $b>1$ ? Select all correct choices.

A
It changes by a constant percentage over equal intervals.
B
It must have a constant positive slope.
C
Its graph has horizontal asymptote $y=0$ when the initial value is positive.
D
Its range includes all real numbers.

True or false

1 point

True or false: A 6% decrease per time period is modeled by multiplying by 1.06 each period.

A
True
B
False

Written response

1 point

What decay factor should be used in a discrete exponential model for a quantity that decreases by 6% each period?

Fill in the blank

1 point

Complete the descriptions of the exponential function $f(x)=ab^x$ : $a$ is the , and $b$ is the .

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1 point

Which two statements correctly identify exponential growth models? Select all correct choices.

A
A discrete growth model can be written as $A(t)=A_0(1+r)^t$ .
B
A discrete decay model always uses $A(t)=A_0(1+r)^t$ .
C
A continuous decay model requires $k>0$ .
D
A continuous growth model can be written as $A(t)=A_0e^{kt}$ .

Written response

1 point

A town's population is modeled by $P(t)=12000(1.025)^t$ , where $t$ is measured in years. What population does the model predict after 10 years? Round to the nearest whole person.

Choose one

1 point

A substance is modeled by $M(t)=500e^{-0.08t}$ , where $M$ is measured in grams and $t$ in hours. Which interpretation is correct?

A
The mass increases by 8 grams per hour.
B
The mass decreases by exactly 8 grams per hour.
C
The mass undergoes continuous decay, and about 309.2 grams remain after 6 hours.
D
The mass becomes zero after 6 hours.

True or false

1 point

True or false: For the continuous decay model $M(t)=500e^{-0.08t}$ , the half-life is $\frac{\ln 2}{0.08}$ hours, approximately 8.66 hours.

A
True
B
False

Choose one

1 point

In $A(t)=P\left(1+\frac{r}{n}\right)^{nt}$ , what does $n=12$ represent when interest is compounded monthly?

A
The principal deposit
B
The number of compounding periods per year
C
The annual interest rate as a percentage
D
The number of years minus one

Open ended

1 point

An account receives a $2,500 deposit at an annual interest rate of 4.8%, compounded monthly. Determine the balance after 3 years and the interest earned. Round both dollar amounts to the nearest cent.

Written response

1 point

Solve the exponential equation $2^{x+1}=16$ for $x$ .

Written response

1 point

Solve $5^x=42$ . Give the value of $x$ rounded to three decimal places. Values within 0.001 of the correct answer are accepted.

Choose one

1 point

A bacterial culture begins with 800 bacteria and grows by 12% per hour according to $N(t)=800(1.12)^t$ . When will the model predict a population of 2,000 bacteria?

A
The population reaches 2,000 after exactly 2.5 hours.
B
The population reaches 2,000 after approximately 1.12 hours.
C
The population never reaches 2,000 because the model is discrete.
D
The population reaches 2,000 after approximately 7.72 hours.

Choose one

1 point

For the exponential function $f(x)=120(0.82)^x$ , which statement correctly describes the function?

A
The function represents exponential growth.
B
The function represents exponential decay.
C
The function is linear.
D
The function has no real-valued domain.

True or false

1 point

True or false: A quantity that increases by the same percentage during each equal time interval is best modeled by a linear function.

A
True
B
False

Choose one

1 point

A savings balance starts at $450 and increases by 6% each year. Which discrete exponential model gives the balance after $t$ years?

A
$A(t)=450(0.06)^t$
B
$A(t)=450(0.94)^t$
C
$A(t)=450(1.06)^t$
D
$A(t)=450(6)^t$

Choose one

1 point

The mass of a substance is modeled by $M(t)=500e^{-0.08t}$ , where $t$ is measured in hours. Which interpretation is correct?

A
The mass is growing continuously because the initial mass is positive.
B
The mass is decaying continuously because $k=-0.08<0$ .
C
The mass is changing linearly because the coefficient is 500.
D
The mass is constant because the exponent contains $t$ .

Choose one

1 point

What is the solution set of $4^x-5(2^x)+4=0$ ?

A
$x=1$ only
B
$x=4$ only
C
$x=-2$ or $x=0$
D
$x=0$ or $x=2$

Fill in the blank

1 point

A city uses an exponential population model that assumes a constant percentage growth rate. Over a long time interval, the model may become unreasonable if food, water, housing, or other resources are .