Free Practice Quiz Question List

10/14 10. Exponential Functions and Applications Online Quiz Questions

Use this free practice quiz with 20 questions to review 10/14 10. Exponential Functions and Applications, test your knowledge, and prepare for your next test or exam.

20 questions

Choose one

1 point

Which statement correctly describes the function $f(x)=3(1.08)^x$ ?

A
It represents exponential decay because the coefficient is positive.
B
It represents exponential growth because the base is greater than 1.
C
It represents linear growth because the exponent is variable.
D
It represents exponential decay because the coefficient is less than 1.

Choose one

1 point

What growth factor corresponds to an annual growth rate of $6\%$ ?

A
1.06
B
0.94
C
6.00
D
1.60

Choose one

1 point

What is the y-intercept of $f(x)=12(0.85)^x$ ?

A
$(12,0)$
B
$(0,1)$
C
$(0,12)$
D
$(1,12)$

Choose all

1 point

Select all statements that correctly describe the continuous model $A(t)=A_0e^{kt}$ .

A
If $k>0$ , the model represents growth.
B
The value of $k$ must always be between 0 and 1.
C
The time unit for $t$ must match the time unit associated with $k$ .
D
The model can represent only discrete, rather than continuous, change.

Choose all

1 point

Select all statements that correctly apply to $A=P\left(1+\frac{r}{n}\right)^{nt}$ when interest is compounded quarterly.

A
Quarterly compounding uses $n=12$ .
B
Quarterly compounding uses $n=4$ .
C
The exponent is always $t+n$ .
D
The exponent in the periodic formula is $nt$ .

True or false

1 point

True or false: The equation $3^{2x-1}=27$ has solution $x=2$ .

A
True
B
False

True or false

1 point

True or false: A quantity that decreases by $15\%$ each period has decay factor $0.85$ .

A
True
B
False

Written response

1 point

Solve $2^x=7$ . Give $x$ rounded to three decimal places. Answers within 0.001 of the correct value are accepted.

Written response

1 point

Classify the model $V(t)=12000(0.85)^t$ as exponential growth or exponential decay.

Fill in the blank

1 point

Complete each rule. For a decimal rate $r$ , the growth factor is , while the decay factor is .

Fill in the blank

1 point

The model $A(t)=A_0e^{kt}$ is called the model.

Open ended

1 point

A deposit of $\$1,200$ earns $4\%$ annual interest compounded quarterly for 6 years. Find the account balance, rounded to the nearest cent, and show the formula and substitutions you use.

Written response

1 point

A bacterial culture starts with 500 cells and grows continuously at $3\%$ per hour. How many cells are present after 8 hours? Give the approximate value to the nearest hundredth; answers within 0.01 are accepted.

Choose one

1 point

A substance has an initial mass of 800 grams and a half-life of 6 years. What mass remains after 18 years?

A
50 grams
B
75 grams
C
100 grams
D
400 grams

Choose one

1 point

An investment follows $A(t)=2500(1.05)^t$ . Approximately when does it reach $\$4,000$ ?

A
Approximately 5.00 years
B
Approximately 9.58 years
C
Approximately 16.00 years
D
Approximately 20.00 years

Choose one

1 point

Which type of behavior is modeled by $f(x)=900(0.85)^x$ ?

A
Exponential growth
B
Exponential decay
C
Linear growth
D
Polynomial growth

True or false

1 point

True or false: In the continuous model $A(t)=A_0e^{kt}$ , a negative value of $k$ represents exponential decay.

A
True
B
False

Written response

1 point

Solve $3^{2x-1}=27$ . Enter the value of $x$ .

Choose one

1 point

For $f(x)=ab^x$ , where $a\neq0$ , which point is the $y$ -intercept?

A
(a, 0)
B
(0, a)
C
(0, b)
D
(b, 0)

Choose one

1 point

Which expression gives the solution to $2^x=7$ ?

A
$\frac{\ln 7}{\ln 2}\approx2.807$
B
$\frac{\ln 2}{\ln 7}\approx0.356$
C
$\frac{\ln 7}{2}\approx0.973$
D
$\frac{\ln 2}{7}\approx0.099$