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.

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.

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.

What does that mean? Example 1: Given the equation: 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: % 50% 100%

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? Initial amount = 50 = a Percentage of growth = 13% =.13 b = 1 + percent = = 1.13

On the same paper as before, write an exponential function with the following characteristics: 4.)Initial amount = 5 Percent of increase = 3% 5.)A population starts with 100 people and grows at 5% per year. 6.)Initial amount = 112 Percent of increase = 200%

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? Initial amount = 5 = a Percentage of growth = 3% =.03 b = 1 + percent = = 1.03

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? Time = 10 years = x

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 (1-15 odds,16, odds)