Exponential Growth & Decay

Exponential Growth & Decay

Lesson 8.7

Growth: goes up in value, use this formula!

y = c(1+r)t 1+r>1

Decay: goes down in value, use this formula!

y = c(1- r)t 1- r <1

Example:

You buy a new 10 speed bike for $150. It loses value at a rate of 15% per year. What is it’s worth in 3 years?Worth = cost(rate)years

w = c(1-0.15)3 (a loss means –15%)

w = 150(.85)3

w = 92.12

The bike was only worth $92.12 in 3 years.

Identify the following as growth or decay

y = 500(1.20)5

y = 375(.078)t

y = 5(1.078)6

y = 30(.99)4

Write a general equation for the following

You purchased a car for $35,000. The minute you drove it off the lot it started going down in value by 1.3%. Write an equation for its value in the future.

You just purchased a painting as an investment and it is suppose to appreciate it value at a rate of 3.65% each year. Write an equation for its value in the future.

V = 35,000(0.987)t

V = P(1.0365)t