Algebra II/ Section 8-1 & 8-2
Name____________________________________
Using the descriptions, determine if each equation is an exponential GROWTH or DECAY equation.
x
x
3
1
x
1. y  4   ________ 2. y  8  7 __________ 3. y  5   _________
8
8
x
4
4. y  8   ____________
3
Exponential growth formula:
a  the initial amount ( amount started with)
y  a(1  r )t
r  percent increase
t  time
(1  r )  the growth factor
EXAMPLE 1: The population of a town in a certain year is 3560 and it increases by about 2% per year. What will
its population be 4 years later?

Since the population started at 3560…….. a=3560

Since it increases by 2% per year …….. r=.02

Since we want to know the population in 4 years…..t=4
y  3560(1  .02)4
y  3853
HW problems – show your work!
5. You deposit $2000 in an account that pays 5% annual interest. Find the balance after 3 years .
a=_____ r=_____
t=_____
6. You have inherited land that was valued at $30,000. The value of the land increases by 5% every year. What
is its value 50 years later?
a=_____ r=______ t=______
7. The student enrollment of a high school was 1240 and increased by 15% per year. What was its enrollment
6 years later?
a=______ r=_______ t=______
8. The population of Winnemucca, Nevada was 6191 in 1990 and increased by 4% each year. What was its
population in 2000?
a=_______ r=_______ t=______
Exponential Decay formula:
y  a(1  r )t
a  the initial amount ( amount started with)
r  percent increase
t  time
(1  r )  the decay factor
EXAMPLE 2: You buy a new sailboat for $15,000. The value of the boat decreases by 11% each year. What will
be it’s value in 3 years?

Since it started at $15,000…….a=15,000

Since its value decreased by 11%.......r=.11

Since we want to know its value in 3 years……..t=3
y  15, 000(1  .11)3
y  10,574.54
HW problems - Show your work!!!
9. For the sailboat in example 2, what will be its value in 5 years?
a=________ r=_______ t=________
10. You drink a beverage with 120 milligrams of caffeine. Each hour, the amount of caffeine in your system
decreases by 12%. How much is left after 2.5 hours?
a=________ r=_________ t=________
11. An adult takes 400 milligrams of ibuprofen. Each hour the amount of ibuprofen in the person’s system
decreases by 29%. How much is left after 1 hour.
a=________ r=_________ t=_________
12. 100 grams of plutonium is stored in a container. How much is left after 20,000 years if plutonium decays at
a rate of .003% per year?
a=_________ r=_________ t=_________