Goal: Write and use models for exponential DEcay

Vocabulary Exponential Decay– when something decreases by the same percent for each unit of time. Examples: The value of a car The number of people living in a town The decrease of an animal population The profit of a company ….

y = C(1-r)t The Formula C is the beginning amount r is the rate (%) t is the time y is the ending amount (what you are looking for)

Rounding Money: round to two places after the decimal People: round to a whole number Animals: round to a whole number

Example #1 You buy a used car for $18,000. The value of the car depreciates at a rate of 12% per year. What is the value of the car in 8 years? C = 18,000 r = 12% = 0.12 t = 8 y = ??? $6473.42

Example #2 Every day the price of a sweater is reduced by 25%. At the beginning it costs $35. What will the sweater cost on the fourth day? C = 35 r = 25% = 0.25 t = 4 y = ??? $11.07

Example #3 In 1993, the population of a town is 1400 people. The population is decreasing at a rate of 8% per year. How many people will there be in the town in 1998? C =1400 r = 8% = 0.08 t = 5 y = ??? 923 people

Practice Worksheet – “8.6 Exponential Decay Practice”

Find the percent 94% y = 500(0.06)5 13% y = 2400(0.87)3 5% 38% 50% 75% y = 500(0.06)5 y = 2400(0.87)3 y = 13(0.95)8 y = 50(0.62)2 y = 200(0.5)3 y = 250(0.25)7

Is it Growth or Decay??? y = 60(1.09)8 y = 200(0.05)8 y = 5200(1.3)8

Homework Worksheet – “8.6 Exponential Decay Homework”