1. Applications of Exponential Functions

2. Population Growth
Population growth can be modeled by the basic form of the exponential function y = abx.
Growth: b > 1
b = “growth factor”
a = “initial amount”
x = time
y = ending amount

3. Population Growth
In 2003, the population of the popular town of Smithville was estimated to be 35,000 people with an annual rate of increase (growth) of about 2.4%.
What is the growth factor?
After one year: 35,000 + (0.024)(35,000)
Factor out 35,000
35,000( ) = 35,000(1.024)
So, the growth factor is 1.024

4. Population Growth
2. Write an equation to model future population growth in Smithville.
y = abx
y = a(1.024)x
So, y = 35,000(1.024)x, where x is the number of years since 2003.

5. Population Growth
3. Use the equation that you’ve written to estimate the population of Smithville in 2007 to the nearest one hundred people.
y = 35,000(1.024)4 = 38, = 38,500

6. Compound Interest What is interest?
Compound Interest: Interest that is earned on both the principal and any interest that has been earned previously.
Balance: The sum of the Principal and the Interest

7. Compound Interest Formula: A: the ending amount
P: the beginning amount (or "principal”)
r: the interest rate (expressed as a decimal)
n: the number of compoundings in a year
t: the total number of years

8. Compound Interest
Jackie deposits $325 in an account that pays 4.1% interest compounded annually. How much money will Jackie have in her account after 3 years?
A = 325( )1(3) 1
A = 325(1.041)3
A = $366.64
Jackie will have $ in her account after 3 years.