1. Exponential Functions,
Growth and Decay
Essential Questions
How do we write and evaluate exponential expressions to model growth and decay situations?
Holt McDougal Algebra 2
Holt Algebra 2

2. Graphing Exponential Growth Functions
Graph the function. State the domain and range.
Move curve 2 units to the right
HA:
and 4 units up
Domain:
All real numbers
Range: 2

3. Graphing Exponential Growth Functions
Graph the function. State the domain and range.
HA:
Move curve 4 units to the left
and down 3 units.
Domain:
All real numbers
Range: 3

4. You can model growth or decay by a constant percent increase or decrease with the following formula:
In the formula, the base of the exponential expression, 1 + r, is called the growth factor. Similarly, 1 – r is the decay factor.

5. Economics Application
Clara invests $5000 in an account that pays 6.25% interest per year. What will the investment be worth in 10 years?
Write a function to model the growth in value of her investment.
f(t) = a(1 + r)t
Exponential growth function.
f(t) = 5000( )10
Substitute 5000 for a and for r and 10 for t.
f(t) = $
Evaluate.

6. Economics Application
In 1981, the Australian humpback whale population was 350 and increased at a rate of 14% each year since then. Write a function to model population growth. What did the population reach in 2011?
Write a function to model the growth in population.
f(t) = a(1 + r)t
Exponential growth function.
f(t) = 350( )30
Substitute 350 for a and 0.14 for r and 30 for t.
f(t) = 17,833
Evaluate. 6

7. Economics Application
A city population, which was initially 15,500, has been dropping 3% a year. Write a function to model population decay. What will be the population in 25 years?
Write a function to model the decay in population.
f(t) = a(1 - r)t
Exponential decay function.
f(t) = 15,500( )25
Substitute 15,500 for a and 0.03 for r and 25 for t.
f(t) = 7,238
Evaluate. 7

8. Economics Application
A motor scooter purchased for $1000 depreciates at an annual rate of 15%. Write a function to model the value of depreciation. What will be the value in 15 years?
Write a function to model the decay in population.
f(t) = a(1 - r)t
Exponential decay function.
f(t) = 1000( )15
Substitute 1000 for a and 0.15 for r and 15 for t.
f(t) = $87.35
Evaluate. 8

9. Lesson 8.1 Practice B 9