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

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

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

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.

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(1 + 0.0625)10 Substitute 5000 for a and 0.0625 for r and 10 for t. f(t) = $9167.68 Evaluate.

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(1 + 0.14)30 Substitute 350 for a and 0.14 for r and 30 for t. f(t) = 17,833 Evaluate. 6

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(1 - 0.03)25 Substitute 15,500 for a and 0.03 for r and 25 for t. f(t) = 7,238 Evaluate. 7

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(1 - 0.15)15 Substitute 1000 for a and 0.15 for r and 15 for t. f(t) = $87.35 Evaluate. 8

Lesson 8.1 Practice B 9