1. Modeling Exponential Functions

2. Warm-Up Write as a decimal. 1) 8% 2) 2.4% 3) 0.01% Evaluate. 4) 36
1) 8%
2) 2.4%
3) 0.01%
Evaluate.
4) 36
5) (34)(43)
6) (24)(23)

3. Exponential Model The basic form of any exponential model is
Where a = initial amount
b = multiplier

4. 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.

5. 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

6. 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
= $
= $

7. 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

8. 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.

9. Compound Interest
The total amount of an investment, A, earning compound interest is
where P is the principal,
r is the annual interest rate,
n is the number of times interest is compounded per year,
and t is the time in years.

10. Example 1
Find the final amount of a $500 investment after 8 years at 7% interest compounded annually, quarterly, and monthly.
compounded annually:
= $859.09
compounded quarterly:
= $871.11
compounded monthly:
= $873.91

11. Practice
Find the final amount of a $2200 investment at 9% interest compounded monthly for 3 years.

12. Assignment
Pg. 430, #14-32 even, 44, 45, 46