Exponential Decay GOAL WRITE AND USE MODELS FOR

Exponential Decay 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 � ….

The Formula y = C(1 -r)t �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 – “Exponential Decay Practice”

Find the Percent �y = 500(0. 06)5 Ø 94% �y = 2400(0. 87)3 Ø 13% �y = 13(0. 95)8 Ø 5% �y = 50(0. 62)2 Ø 38% �y = 200(0. 5)3 Ø 50% �y = 250(0. 25)7 Ø 75%

Is it Growth or Decay? ? ? � y = 60(1. 09)8 �Growth �y = 200(0. 05)8 �Decay � y = 5200(1. 3)8 �Growth � y = 32(1. 07)8 �Growth � y = 560(0. 13)8 �Decay

Homework �Worksheet – “Exponential Decay Homework”