Lesson 8.5 and 8.6 Objectives: Exponential Growth and Exponential Decay. Exponential Growth: is growth when the quantity increases by the same percent in each unit of time. Exponential Growth Formula: Time Amount after increase Rate of increase Amount before increase This growth function is used to find growth in population, interest, or any quantity that grows exponentially.

The longer you invest the more interest you earn! You deposit $500 in a bank account that pays 6% interest compounded yearly. Find the value of the account after 1 year, 2 years, 3 years, 20 years. Example: Use C = 500 r = .06 t = 1,2,3,20 1 year 2 years 3 years 20 years y = 500(3.20713) y = $595.508 y = $1603.57 The longer you invest the more interest you earn!

Exponential Decay: is decrease of a quantity by the same percent over a period of time. Things that have exponential decay: medication, radioactive waste, bodies, car value(depreciation). Time Decay formula Rate of decrease Amount after decrease Initial amount before decrease Example: A popular medication loses 23% of its effectiveness each hour. Find how much of the 200 mg of each pill is working after 5 hours. y = 200(.2706) y = 54.13mg

Example: Depreciation y = 20000(.5717) y =$11,435.74 The average new car loses 17% of its value each year. Find the value of a $20,000 car after 3 years. Example: Depreciation y = 20000(.5717) y =$11,435.74