Exponential Growth and Decay Word Problems

Exponential Growth vs. Decay Exponential Decay y = a∙bx y = a∙bx 0 < b < 1 b > 1

Exponential Growth and Decay Models y = a(1 + r)x a = starting amount r = rate r is positive for growth r is negative for decay

Growth or decay? What percentage? y = 67(1.06)x y = -98(.87)x y = 300(1.27)x y = 142(.35)x y = 5(2)x

Example 1: iPads y = a(1 + r)x The value of an iPad decreases at 35% per year. If the starting price of the iPad is $500, write the exponential function. How much will the iPad be worth after 5 years? When can you buy the iPad for $5?

Example 2: Forest y = a(1 + r)x Suppose the acreage of forest is decreasing by 2% per year because of development. If there are currently 4,500,000 acres of forest, how much forest land will there be in 6 years?

Example 3: Investing y = a(1 + r)x Find a bank account balance to the nearest dollar, if the account starts with $100, has an annual rate of 4%, and the money is left in the account for 12 years. If you wanted to buy a new gaming system for $250, when will you have enough?

Example 4: Car Salesman y = a(1 + r)x Dave bought a car 8 years ago for $5400. To buy a similar car today would cost $12,500. Assuming a steady rate of increase, what was the yearly rate of inflation?

Half Life Some unstable substances, like plutonium, decay over time. To measure the rate of decay, scientists refer to their “half life.” The half life is the time it takes for half the initial amount of the substance to decay.

Example 5: DDT y = a(1 + r)x The pesticide DDT was widely used in the United States until its ban in 1972. Write an equation that models the 15 year half-life of 100 grams of DDT. How much DDT would be remaining after 45 years?

Example 6: 228Ac y = a(1 + r)x 228Ac has a half life of 6.13 hours. Write an equation that models the half life of a 5 mg sample. How much 228Ac would be remaining after one day?