Goal: Write and use models for exponential growth

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 ….

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)

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

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

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% = 0.065 t = 5 y = ??? $1370.09

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

Example #4 A company has 50 employees in 2000. 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

Example #5 A population of 20 rabbits is released into a wild-life region in 1990. The population increases by 58% each year. What is the population 1995? C = 20 r = .58 t = 5 y = ??? 197rabbits

Practice Worksheet – “8.5 Exponential Growth Practice”

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

Homework Worksheet – “8.5 Exponential Growth Homework”