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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=.8628t • log 0.2=t log 0.8628 • t=log 0.2/log0.8628 • 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-0.1372t • ln 0.2= -0.1372t • 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=7000e0.04*70 • Y=109001 y=115113
