Exponential Growth and Decay  Exponential Decay Depreciation of value and radioactive decay are examples of exponential decay. When a quantity decreases by a fixed percent each time period, the amount of the quantity after t time periods is given by y=a(1- r) t, where a is the initial amount and r is the percent decrease expressed as a decimal. Another exponential decay model often used by scientists is y=ae -kt, where k is a constant.

Exponential Growth and Decay  A CPA is computing the present value of a truck for a client. The truck was bought for $ years ago. What is the current value of the truck if the depreciation rate is 13.72%.  Y=50000( ) 4  27708

Exponential Growth and Decay  After how many years will the truck value be $10000  10000=50000( ) t .2=.8628 t  log 0.2=t log  t=log 0.2/log  10.9 years…11 years

Exponential Growth and Decay  If it was based on a continuous depreciation, how many years will it take for the same situation  1/5=e t  ln 0.2= t  t= ln 0.2/  t=11.72

Exponential Growth and Decay  What are the growth formulas ?  y = a(1 + r) t and y = ae +kt,

Exponential Growth and Decay  Bills grandfather bought his house in 1942 for $7000. If the house had an average appreciation rate of 4%, what is the current value of the house? (compute by annual rate and continual)  y=7000(1+.04) y=7000e 0.04*70  Y=109001y=115113

Exponential Growth and Decay