11 terms

# Exponential Growth and Decay Practice

Growth and Decay Practice
###### PLAY
The \$1,000 invested in a simple savings account earns 6% interest each year.
a) Write an equation.
b) How much money will be in account after 10 years?
a) y = 1,000 (1.06)ⁿ

b) \$1,790.85
Janelle invests \$2,000 in a savings account, which earns 5% interest per year.

a) Write an equation.
b) Approximately how many years will it take for the original amount to double in value?
a) y = 2,000 (1.05)ⁿ

b) 15 years ≈\$4,157.86
The population of Tribetts (insect) decreases by 30% each year. The starting population was 10,000.

a) Write an equation.
b) Make a table showing the number of Tribetts (insect) at the end of the first five years.
c) In what year will there first be fewer than 1,000 Tribetts (insect).
a) y = 10,000 (.70)ⁿ

b) Years-------Tribetts
0 ----------10,000
1----------- 7,000
2------------ 4,900
3------------- 3,430
4-------------2,401
5-------------1,681

c) 7 years ≈824
Write an exponential equation, find the amount after the specified time.

Suppose the acreage (quantity of acres) of forest is decreasing by 2% per year because of development. If there are currently 4,500,000 acres of forest, determine the amount of forest land after 6 years.
4,500,000 (.98)⁶ = \$3,986,290
Write an exponential equation, find the amount after the specified time.

A \$10,500 investment has a 15% loss each year. Determine the value of the investment after 4 years.
10,500 (.85)⁴ = \$5981.07
y = 40,000 (1.34)ⁿ

What is the initial amount, growth factor, growth rate (% increase)?
Initial amount = 40,000
Growth Factor = 1.34
Growth Rate = 34%
y = 19 (.86)ⁿ

What is the initial amount, decay factor, decay rate?
Initial amount = 19
Decay Factor = .86
Decay Rate = 14%
Does the equation model growth or decay?

y = 300 (1.7)ⁿ
Growth, because exponential factor is greater than 1.
Does the equation model growth or decay?

y = 9 (1.02)ⁿ
Growth, because exponential factor is greater than 1.
Does the equation model growth or decay?
y = 657 (.8)ⁿ
Decay, because exponential factor is less than 1.
Does the equation model growth or decay?

y = 56 (.04)ⁿ
Decay, because exponential factor is less than 1.