Free Printable 7 Review Power Functions

1.

Convert to Radical Form: $y^{\frac{1}{3}}$

a)

b)

$y^3$

c)

d)

$\frac{1}{3}y$

2.

Simplify:

a)

2

b)

8

c)

16

d)

32

3.

A bond paying 5.4% interest compounded monthly for 8 years has matured giving the investor $5000. How much did the investor pay for the bond 8 years ago? (Round to the nearest penny)

(a)

4.

What is the constant ratio of this geometric sequence: 15, 45, 135, . . . ?

(a)

5.

Convert into Rational Exponent Form: $\sqrt{7}$

a)

$7^2$

b)

$7^{-2}$

c)

$7^{\frac{1}{2}}$

d)

$7^{-\frac{1}{2}}$

6.

(2x⁷)³

a)

6x²¹

b)

8x²¹

c)

6x¹⁰

d)

8x¹⁰

7.

Determine if the following sequence is arithmetic or geometric.

15, 13, 11, 9, 7, ...

a)

Arithmetic

b)

Geometric

8.

There are approximately $3.36\ x\ 10^8$ people in the US. and approximately $3.155\ x\ 10^{11}$ pounds of food eaten in a year. How many pounds of food per person is eaten on average each year?

a)

$9.39\ x\ 10^2$

b)

$9.39\ x\ 10^3$

c)

$1.065\ x\ 10^2$

d)

$1.065\ x\ 10^2$

9.

Simplify (2m⁴)(5m²)

a)

10m⁶

b)

10m⁸

c)

7m⁶

d)

7m⁸

10.

Suppose a ball is dropped from a height of 10 feet, and it bounces up to 70% of its previous height after each bounce. Find the height of the ball bounces to after its fourth bounce. (round to the nearest tenth)

(a)

11.

Solve for a:

$a^{-\frac{2}{5}}=9$

a)

$243$

b)

$\frac{1}{243}$

c)

$59049$

d)

$\frac{1}{59049}$

12.

Your $54,200 four-year car loan is at 9.2% compounded monthly. What will you have paid for your car after four years? Round to the nearest dollar.

(a)

13.

Given: $f\left(x\right)=x^n$

where n is a positive even number. In which quadrants is the graph?

a)

I

b)

II

c)

III

d)

IV

14.

Solve for x:

$x^{-\frac{3}{2}}=\frac{1}{64}$

(a)

15.

True or False:

The domain of even functions is all real numbers.

a)

True

b)

False

16.

Write the explicit equation for the geometric sequence: 15, 45, 135, . . . ?

a)

$t\left(n\right)=3\left(5\right)^n$

b)

$t\left(n\right)=5\left(3\right)^n$

c)

$t\left(n\right)=15\left(3^{\left(n\right)}\right)$

d)

$t\left(n\right)=15\left(5\right)^n$

17.

Solve for x:

$2x^{\frac{2}{3}}=50$

(a)

18.

Which of the following recursive formulas represents the given sequence.

7, 14, 28, 56, 112, ...

a)

$a_1=7$ , $a_n=a_{\left(n-1\right)}+7$

b)

$a_1=7$ , $a_n=7a_{\left(n-1\right)}$

c)

$a_1=7$ , $a_n=2a_{\left(n-1\right)}$

d)

$a_1=7$ , $a_n=a_{\left(n-1\right)}+14$

19.

True or False:

$3i$ is a fourth root of 81.

a)

True

b)

False

20.

$3b^{-3}\ \left(\ -2b^2\right)$

a)

$6b^2$

b)

$\frac{6}{b}$

c)

$-6b$

d)

$-\frac{6}{b}$

21.

True or False:

Odd functions have reflection symmetry over the y axis.

a)

True

b)

False

22.

$7b^3\ \cdot\ 3b^2$

a)

$10b^6$

b)

$21b^6$

c)

$10b^5$

d)

$21b^5$

23.

Write an equation of the power function that goes through the point (2, 32).

a)

$y=x^3$

b)

$y=x^4$

c)

$y=x^5$

d)

$y=x^6$

24.

Solve for x:

$x^{-\frac{5}{2}}=41$

a)

0.0000929

b)

0.2264

c)

10763

d)

4.417

25.

Find the recursive formula for the sequence. $1,\ 3,\ 9,\ 27,...$

Given:

$g_1=1$

a)

$g_n=3g_{n-1}$

b)

$g_n=g_{n-1}\cdot1+3$

c)

$g_n=1\cdot3^{n-1}$

d)

$g_n=3\cdot1^{n-1}$

26.

Determine if the following sequence is arithmetic or geometric.

200, 100, 50, 25, ...

a)

Arithmetic

b)

Geometric

27.

$\frac{\left(4x^2y\right)^{-1}}{\left(2xy^2\right)}$

a)

$\frac{1}{8x^3y^3}$

b)

$\frac{2x}{y^3}$

c)

$\frac{2}{x^3y^3}$

d)

$\frac{1}{8xy}$

28.

The next term of the geometric sequence

4, 16, 64, ...

is

(a)

29.

Will deposits $1650 for three years at 3% interest, compounded daily. What is his ending balance?

a)

$1,700.25

b)

$4,056.85

c)

$2,103.87

d)

$1,805.38

30.

Write the explicit equation for the geometric sequence:

10, 20, 40, 80, ...

a)

$t\left(n\right)=5\left(2\right)^n$

b)

$t\left(n\right)=2\left(5\right)^n$

c)

$t\left(n\right)=2\left(10\right)^n$

d)

$t\left(n\right)=10\left(2\right)^n$

31.

Given: $f\left(x\right)=x^n$

where n is a positive odd number. In which quadrants is the graph?

a)

I

b)

II

c)

III

d)

IV

32.

A vacuum pump removes 10% of the air from a chamber with each stroke. Find a formula that gives the percent of air that remains in the chamber after the nth stroke.

a)

$P\left(n\right)=\left(.9\right)^n$

b)

$P\left(n\right)=\left(.1\right)^n$

33.

$\left(2x^{-5}\right)\left(3x^4\right)$ =

a)

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

b)

$\frac{5}{x}$

c)

$\frac{-6}{x}$

d)

$\frac{6}{x}$

34.

$a^2\left(\frac{ab^3}{b^2}\right)b^5$

a)

$a^2b^6$

b)

$a^2b^4$

c)

$a^3b^{-2}$

d)

$a^3b^6$

35.

$\left(-3x^7\right)^2$ =

a)

$9x^{14}$

b)

$6x^9$

c)

$6x^{14}$

d)

$-9x^7$

7 Review Power Functions

Total questions: 35

Worksheet time: 56mins

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