EXPONENTIAL GROWTH AND DECAY WORD

PROBLEMS

Exponential Growth vs. Decay

Exponential Growthy = a∙bx

b > 1

Exponential Decayy = a∙bx

0 < b < 1

6

4

2

-2

-5

f x = 2x

8

6

4

2

-5 5

h x = 0.5x

Exponential Growth and Decay Models

r = rater is positive for growth

r is negative for decay

y = a(1 ± r)x

a = starting amount

For each example:a) Tell the initial amount

b)Growth or decay? C) What percentage?

1. y = 67(1.06)x

2. y = -98(.87)x

3. y = 300(1.27)x

4. y = 142(.35)x

5. y = 5(2)x

Example 1: iPadsThe 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?

y = a(1 ± r)x

Example 2: ForestSuppose 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: InvestingFind 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.

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 4: DDTThe 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 5:228Ac 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?