1. Exponential Growth and Decay
Objectives:
Determine the multiplier for exponential growth and decay
Write and evaluate exponential expressions to model growth and decay situations

2. Modeling Bacteria Growth
Time (hr) 1 2 3 4 5 6
Population 25 50
100
200
400
800
1600
Write an algebraic expression that represents the population of bacteria after n hours.
The expression is called an exponential expression because the exponent, n is a variable and the base, 2, is a fixed number.
The base of an exponential expression is commonly referred to as the multiplier.

3. Example 1
Find the multiplier for each rate of exponential growth or decay.
a) 9% growth
100%
+ 9%
= 109%
= 1.09
b) 0.08% growth
100%
+ 0.08%
= % =
c) 2% decay
100%
- 2%
= 98%
= 0.98
d) 8.2% decay
100%
- 8.2%
= 91.8%
= 0.918

4. Example 2
Suppose that you invested $1000 in a company’s stock at the end of 1999 and that the value of the stock increased at a rate of about 15% per year.
Predict the value of the stock, to the nearest cent, at the end of the years 2004 and 2009.
Since the value of the stock is increasing at a rate of 15%, the multiplier will be 115%, or 1.15
= $
= $

5. Example 3
Suppose that you buy a car for $15,000 and that its value decreases at a rate of about 8% per year. Predict the value of the car after 4 years and after 7 years.
Since the value of the car is decreasing at a rate of 8%, the multiplier will be 92%, or 0.92
= $10,745.89
= $8,367.70

6. Practice
A vitamin is eliminated from the bloodstream at a rate of about 20% per hour. The vitamin reaches a peak level in the bloodstream of 300 mg. Predict the amount, to the nearest tenth of a milligram, of the vitamin remaining 2 hours after the peak level and 7 hours after the peak level.