Exponential Functions Growth and Decay Growth and How

Exponential Functions, Growth, and Decay Growth and • How do we write and evaluate exponential expressions to model growth and decay situations? Holt. Mc. Dougal Algebra 2 Holt

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

Exponential Functions, Growth, and Decay 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: Holt Mc. Dougal Algebra 2

Exponential Functions, Growth, and Decay 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. Holt Mc. Dougal Algebra 2

Exponential Functions, Growth, and Decay Economics Application 3. 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. Holt Mc. Dougal Algebra 2

Exponential Functions, Growth, and Decay Economics Application 4. 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. Holt Mc. Dougal Algebra 2

Exponential Functions, Growth, and Decay Economics Application 5. 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. Holt Mc. Dougal Algebra 2

Exponential Functions, Growth, and Decay Economics Application 6. 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. Holt Mc. Dougal Algebra 2

Exponential Functions, Growth, and Decay Lesson 8. 1 Practice B Holt Mc. Dougal Algebra 2