Chapter 8: Exponents and Exponential Functions

Zero & Negative Exponents

100

Simplify the expression so it has no negative exponents:

b^-4c⁰d⁶

(d^6) / (b^4)

200

Simplify the expression so it has no negative exponents:

1 /( p^2q^-4r^-1

(q^4r) / (p^2)

300

Simplify the expression so it has no negative exponents:

7^-2y^-4z

z / (49y^4)

400

Evaluate the expression for r = -3 &  s = 5:

5r³s^-1

-27

500

Suppose your allowance doubles every week. This week you receive $2.56. How much will your allowance be 3 weeks from now? How much was your allowance 3 weeks ago?

$20.48 ; $0.32

Scientific Notation

100

Convert the following to scientific notation:

567,900,000

5.679 x 10⁸

200

Convert the following to scientific notation:

0.000000007981

7.981 x 10^-9

300

Simplify:

(7.3 x 10⁷) x (1.12 x 10^-2)

8.176 x 10⁵

400

The space probe Voyager 2 traveled 2 million, seven hundred ninety-three thousand miles. Write that number in scientific notation.

2.793 x 10⁶ miles

500

Write the following numbers in standard form:

3.2 x 10^-6
1.685 x 10¹²

0.0000032
1,685,000,000,000

Multiplication/Division Properties of Exponents

100

Simplify without negative exponents:

(3x³y^-2)⁴

(81x^12) / y^8

200

Find the volume of a cube with side length of 4/5 m.

 64/125  m³

300

Evaluate the following expression for m = 2, t = -3,
w = 4, & z = 0:

w^mw^z

16

400

Evaluate the following expression for m = 2, t = -3,
w = 4, & z = 0:

w^m x t^m

144

500

The speed of sound is approximately 1.2 x 10³ km/h. How long does it take for sound to travel 7.2 x 10² km?

36 minutes

Geometric Sequences & Exponential Functions

100

How do you know if a sequence is a geometric sequence?

The is a common ratio to get from one term to the next.

200

Find the common ration and the next two terms of the following sequence:

12, 18, 27, ...

x 1.5; 40.5, 60.75

300

Find the common ratio and the next two terms of the following sequence:

30, 10, 10/3, ...

x (1/3); 10/9, 10/27

400

What is the formula for a geometric sequence?

A(n) = a(r ^n-1)

500

Find the 8th term of the following geometric sequence, (what is the exact number):

2, 3, 4.5, ...

34.171875

Exponential Growth & Decay

100

How can you determine if it is an exponential growth or exponential decay?

If the growth/decay factor is between 0 and 1, it is a decay. If the growth/decay factor is larger than 1, it is a growth.

200

The function y = 25(0.80^x) models the amount y of a 25-mg dose of medicine remaining in the bloodstream after x hours. How many milligrams (to the nearest tenth) of medicine remain in the bloodstream after 5 hours?

about 8.2 mg

300

Write the exponential decay for the following situation and the find the amount.

$3000 investment, 8% loss each year for 3 years

y = 3000(0.92)^x
$2336.06

400

Write the exponential growth for the following situation and the find the amount.

$200 principal, 4% compounded annually for 5 years

y = 200(1.04)^x
$243.33

500

Write the exponential growth for the following situation and the find the amount.

You deposit $520 in an account with 4% interest compounded monthly. What is the balance after 5 years?

y = 520(1 + (.04/12))^5*12
$634.92