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Exploring Exponential Growth and Decay Models in Economics Applications

Learn to model growth and decay scenarios using exponential functions. Practice evaluating investments, population growth, and depreciation. Understand the concepts of growth factors and decay rates. Apply these principles to real-world examples in economics.

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Exploring Exponential Growth and Decay Models in Economics Applications

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  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. HA: Move curve 2 units to the right and 4 units up All real numbers Domain: Range:

  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. All real numbers Domain: Range:

  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 – ris 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. Exponential growth function. f(t) = a(1 + r)t 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.

  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. Exponential growth function. f(t) = a(1 + r)t 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.

  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. Exponential decay function. f(t) = a(1 -r)t 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.

  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. Exponential decay function. f(t) = a(1 -r)t 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.

  9. Lesson 8.1 Practice B

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