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 $50000 4 years ago. What is the current value of the truck if the depreciation rate is 13. 72%. § Y=50000(1 -. 1372)4 § 27708

Exponential Growth and Decay § After how many years will the truck value be $10000 § § § 10000=50000(1 -. 1372)t. 2=. 8628 t log 0. 2=t log 0. 8628 t=log 0. 2/log 0. 8628 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-0. 1372 t § ln 0. 2= -0. 1372 t § t= ln 0. 2/-0. 1372 § 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)2012 -1942 y=7000 e 0. 04*70 § Y=109001 y=115113

Exponential Growth and Decay