Free Printable Exponentials Practice Test

1.

How would we simplify this expression?

3^4\cdot3^2\cdot3^3

a)

Multiply the exponents to get $3^{24}$

b)

Add the expoenenets to get $3^9$

c)

Multiply the bases and add the exponents to get $27^9$

d)

Multiply the bases and multiply the exponents to get $27^{24}$

2.

$\frac{5^3}{5^5}$

Simplify the expression into the most simplified form.

a)

$5^{-2}$

b)

$5^2$

c)

$\frac{1}{25}$

d)

$25^2$

3.

What is $15^0$ ?

(a)

4.

Simplify $4\left(4^2\right)^5$

a)

$4^8$

b)

$4^7$

c)

$4^{10}$

d)

$4^{11}$

5.

Simplify

a)

$x^{\frac{3}{4}}$

b)

$x^{\frac{1}{3}}$

c)

$x^{\frac{1}{4}}$

d)

$x^{\frac{4}{3}}$

6.

Simplify

a)

$6^{\frac{1}{3}}$

b)

$6^{\frac{1}{2}}$

c)

$6^{-\frac{1}{3}}$

d)

$6^{-2}$

7.

Is the sequence arithmetic or geometric? And what is it's formula?

32, 30, 28, 26, .....

a)

Arithmetic: $f\left(n\right)=32\ -2n$

b)

Geometric: $f\left(n\right)=32\left(0.5\right)^n$

c)

Arithmetic: $f\left(n\right)=34-2n$

d)

Arithmetic: $f\left(n\right)=f\left(n-1\right)+2$

8.

Write an equation for a line going through the points:

(1, 14) (2, 7) (3, 3.5)

a)

$y=14\left(.5\right)^x$

b)

$y=14\left(.5\right)^{\left(x+1\right)}$

c)

$y=28\left(.5\right)^x$

d)

$f\left(x\right)\ =\ f\left(x-1\right)+0.5$

9.

Marco is studying a type of mold that grows at a fast rate. He created the function $f\left(x\right)=345\left(1.30\right)^x$ to model the number of mold spores per week. What does the 1.30 represent? How many mold spores are there after 4 weeks?

a)

1.30 represents the 30% of weekly growth; and there are 985 mold spores.

b)

1.30 represents the 30% of weekly growth; and there are 345 mold spores.

c)

1.30 represents the number of mold spores grown in a given week; and there are 448 mold spores.

d)

130 represents the number of mold spores Marco had at the beginning of the study; there are 985 mold spores.

10.

The table above shows the number of contestants each round in a talent competition on television. The competition had five elimination rounds. After each elimination, only one-third of the contestants were sent to the next round.

Compute the average rate of change of f(x) from x = 1 to x = 4

a)

-78

b)

-234

c)

78

d)

234

11.

The number of subscribers y to a newspaper after t years is shown below:

$y=75\left(0.95\right)^t$

Which conclusion is correct about the number of subscribers to the newspaper?

a)

It increased by 75% each year

b)

It decreased by 75% each year

c)

It increased by 5% each year

d)

It decreased by 5% each year

12.

The table above shows the functions to represent the sale f(t), in thousands, of four companies in t years.

Which of the following companies showed an exponential growth in sale?

a)

Company A and Company B

b)

Company B and Company C

c)

Company A and Company D

d)

Company C and Company D

13.

Sophia invested some money in a bank at a fixed rate of interest compounded annually. The equation below shows the value of her investment after x years:
$f\left(x\right)=500\left(1.05\right)^x$
What was the average rate of change of the value of Sophia's investment from the second year to the fourth year?

a)

14.13 dollars per year

b)

28.25 dollars per year

c)

50.00 dollars per year

d)

56.50 dollars per year

14.

The price of silver has increased by 15% per year from 2000. In the year 2000, Harry bought a silver bowl for $190. Which of the following functions f(x) can be used to represent the price of the bowl x years after 2000?

a)

$f\left(x\right)=190\left(0.85\right)^x$

b)

$f\left(x\right)\ =\ 190\left(1.15\right)^x$

c)

$f\left(x\right)\ =\ 15\left(190\right)^x$

d)

$f\left(x\right)\ =\ 15\left(.85\right)^x$

15.

Which statement best describes the effect of replacing the function $f\left(x\right)\ =\ 2^{\left(x-2\right)}$ with the function $g\left(x\right)=2^{\left(x+5\right)}$ ?

a)

The graph shifts 7 units left.

b)

The graph shifts 5 units left.

c)

The graph shifts 2 units up.

d)

The graph shifts 3 units up.

Exponentials Practice Test

Total questions: 15

Worksheet time: 1hrs 15mins

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