1. Goal: Write and use models for exponential growth

2. Vocabulary
Exponential Growth – when something increases by the same percent for each unit of time.
Examples:
Interest in a bank account
The number of people living in a town
The growth of an animal population
The profit of a company ….

3. y = C(1+r)t The Formula C is the beginning amount r is the rate (%)
t is the time
y is the ending amount (what you are looking for)

4. Rounding Money: round to two places after the decimal
People: round to a whole number
Animals: round to a whole number

5. Example #1
You deposit $500 in an account that pays 8% annual interest compounded yearly. What is the account balance after 6 years? C = 500 r = 8% = 0.08 t = 6 y = ??? $793.44

6. Example #2
You deposit $1000 in an account that pays 6.5% annual interest compounded yearly. What is the account balance after 5 years? C = 1000 r = 6.5% = t = 5 y = ??? $

7. Example #3
A new catfish typically weighs about 0.3 grams. It increases by about 10% each day. What will it weigh after 30 days? C =0.3 r = 10% = 0.10 t = 30 y = ??? 5.2 grams

8. Example #4
A company has 50 employees in The number of employees increases by 50% each year. How many employees are there in 2004? C = 50 r = 50% = 0.50 t = 4 y = ??? 253 employees

9. Example #5
A population of 20 rabbits is released into a wild-life region in The population increases by 58% each year. What is the population 1995? C = 20 r = .58 t = 5 y = ??? 197rabbits

10. Practice
Worksheet – “8.5 Exponential Growth Practice”

11. Find the percent 60% y = 500(1.6)5 2% y = 2400(1.02)3 0.4%
90% 5%
4.5%
y = 500(1.6)5
y = 2400(1.02)3
y = 13(1.004)8
y = 50(1.9)2
y = 200(1.05)3
y = 250(1.045)7

12. Homework
Worksheet – “8.5 Exponential Growth Homework”