Check it out! Domain and Range of Exponential Functions

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Check it out! Domain and Range of Exponential Functions http://www.walch.com/wu/09006 Domain and Range of Exponential Functions

What inputs would make sense for this function? Katya put $2,000 into a savings account that gives 6% interest, compounded annually. The investment’s value grows according to the function f(x) = 2000 • 1.06x over the course of 7 years, where x represents the number of years the investment has been growing and f(x) represents the value of the investment. What inputs would make sense for this function? What is the initial value of the investment? What is the value of the investment after 7 years? Domain and Range of Exponential Functions

What inputs would make sense for this function? In the function f(x) = 2000 • 1.06x, x represents years. Because the interest is compounded annually, the inputs of x should be whole numbers. Additionally, the investment was growing over 7 years, so the inputs should start at x = 0 and end at x = 7. The possible inputs are: {0, 1, 2, 3, 4, 5, 6, 7} Domain and Range of Exponential Functions

What is the initial value of the investment? The initial value of the investment is the $2,000 that Katya deposited, which corresponds to x = 0 in the function. Domain and Range of Exponential Functions

What is the value of the investment after 7 years? To find the value of the investment after 7 years, evaluate the function for x = 7: f(x) = 2000 • 1.06x Original function f(7) = 2000 • 1.06(7) Substitute 7 for x. f(7) ≈ 2000 • 1.50363 Evaluate the exponent. f(7) ≈ 3007.26 Simplify. The value of the investment after 7 years is $3,000.26. Connection to the Lesson Students will use function notation with exponential functions. Students will identify a domain that makes sense for the problem context. Students will identify the endpoints of a range. Domain and Range of Exponential Functions