Exponential Function Review Part 2

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What is an exponential function?

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An exponential function is a mathematical function of the form f(x) = a(b^x), where 'a' is a constant, 'b' is the base (a positive real number), and 'x' is the exponent.

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What does it mean for a function to exhibit exponential growth?

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Exponential growth occurs when the growth rate of a value is proportional to its current value, typically represented by a base greater than 1 in the function f(x) = a(b^x).

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What does it mean for a function to exhibit exponential decay?

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Exponential decay occurs when the value decreases at a rate proportional to its current value, typically represented by a base between 0 and 1 in the function f(x) = a(b^x).

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How do you calculate the future value of an investment with exponential growth?

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Use the formula A = P(1 + r)^t, where A is the amount of money accumulated after n years, P is the principal amount, r is the rate of interest, and t is the time in years.

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How do you calculate the future value of an investment with exponential decay?

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Use the formula A = P(1 - r)^t, where A is the amount remaining after time t, P is the initial amount, r is the decay rate, and t is the time.

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What is the decay factor in exponential decay?

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The decay factor is calculated as 1 - r, where r is the decay rate. For example, if the decay rate is 8%, the decay factor is 0.92.

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What is the growth factor in exponential growth?

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The growth factor is calculated as 1 + r, where r is the growth rate. For example, if the growth rate is 25%, the growth factor is 1.25.

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How can you identify exponential decay from a function?

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In the function f(x) = a(b^x), if 0 < b < 1, the function represents exponential decay.

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How can you identify exponential growth from a function?

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In the function f(x) = a(b^x), if b > 1, the function represents exponential growth.

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What is the formula for exponential growth?

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The formula for exponential growth is f(x) = a(b^x), where 'a' is the initial amount and 'b' is the growth factor.