Review:An exponential function is any function of

the form:

where a ≠ 0, b ≠ 1, and b > 0.

• If b > 1, the graph is increasing.• If 0 < b < 1, the graph is decreasing.• If b = 1, the graph is a horizontal line.• The farther b gets from 1, the steeper the

graph.

xy a b

Section 8.2

Exponential Growth

Exponential functions that are increasing are called exponential growth functions.

• a is the initial amount. • b (the base) is the growth factor.

• x (the exponent) is the number of increases.

xy a b

In many real-life problems, there is a percentage

increase/decrease.

Growth Factor

• The growth factor (b) is equal to:

1 + the percent increase

• Conversely, the percent increase can be found by subtracting 1 from the growth factor.

xy a b

What does that mean?

Example 1: Given the equation:xy a b 20 1.45xy

a = 20, which is the initial amount.b = 1.45, which is the growth factor.

To find the percent, subtract 1:

1.45 – 1 = .45 = 45%

On a separate sheet of paper, find the following. Keep the paper.

1.) initial amount:percent increase:

2.)

initial amount: percent increase:

3.)initial amount:percent increase:

10 1.15xy

100 1.5xy

2xy

10

100

1

15%

50%

100%

xy a b

Write an exponential equation:Example #2

Suppose the population in a village is 50 people. If the population is increasing at a rate of 13% every year, what is the equation that represents the situation?

xy a b Initial amount = 50 = a

Percentage of growth = 13% = .13

b = 1 + percent = 1 + .13 = 1.1350 1.13xy

On the same paper as before, write an exponential function with the following characteristics:

4.) Initial amount = 5Percent of increase = 3%

5.) A population starts with 100 people and grows at 5% per year.

6.) Initial amount = 112Percent of increase = 200%

(5)(1.03)xy

(100)(1.05)xy

(112)(3.00)xy

Example 3:Suppose that the rate of inflation over the past 10 years has been 3% per year. If 10 years ago an item cost $5, how much should it cost today?

xy a b Initial amount = 5 = a

Percentage of growth = 3% = .03

b = 1 + percent = 1 + .13 = 1.03

5 1.03xy

Suppose that the rate of inflation over the past 10 years has been 3% per year. If 10 years ago an item cost $5, how much should it cost today?

xy a b Time = 10 years = x

5 1.03xy 105(1.03)y

Write an exponential equation to model the growth function in the situation and then solve the problem.

7.) Suppose that the number of bacteria in a shoe increases by 20% every day. If there are 5000 bacteria in the shoe on Monday, how many bacteria will be in the shoe on Friday?

Turn in your papers when you are done!

Homework 8.2(Due at the beginning of next class.)

Page 370-372

(1-15 odds,16, 23-29 odds)