Exponential Growth and Decay

1
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 ya(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 yae-kt, where k is a constant.

2
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.
• Y50000(1-.1372)4
• 27708

3
Exponential Growth and Decay

• After how many years will the truck value be
  10000
• 1000050000(1-.1372)t
• .2.8628t
• log 0.2t log 0.8628
• tlog 0.2/log0.8628
• 10.9 years11 years

4
Exponential Growth and Decay

• If it was based on a continuous depreciation, how
  many years will it take for the same situation
• 1/5e-0.1372t
• ln 0.2 -0.1372t
• t ln 0.2/-0.1372
• t11.72

5
Exponential Growth and Decay

• What are the growth formulas ?
• y a(1 r)t and y aekt,

6
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)
• y7000(1.04)2012-1942 y7000e0.0470
• Y109001 y115113

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Exponential Growth and Decay