Exponential Functions

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What is an exponential function?

Back

An exponential function is a mathematical function of the form f(x) = a(b^x), where 'a' is a constant, 'b' is a positive real number, and 'x' is the exponent. It shows rapid growth or decay.

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What does the base of an exponential function represent?

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The base of an exponential function indicates the growth (if greater than 1) or decay (if between 0 and 1) rate of the function.

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What is the general form of an exponential growth function?

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The general form of an exponential growth function is f(x) = a(b^x) where b > 1.

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What is the general form of an exponential decay function?

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The general form of an exponential decay function is f(x) = a(b^x) where 0 < b < 1.

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How do you identify exponential growth from a function?

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Exponential growth can be identified if the base of the function is greater than 1.

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How do you identify exponential decay from a function?

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Exponential decay can be identified if the base of the function is between 0 and 1.

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What is the y-intercept of an exponential function f(x) = a(b^x)?

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The y-intercept is the value of f(0), which equals 'a'.

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What does the term 'initial amount' refer to in exponential functions?

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The initial amount refers to the value of 'a' in the function f(x) = a(b^x), representing the starting value before growth or decay.

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What is the effect of increasing the base 'b' in an exponential growth function?

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Increasing the base 'b' results in a faster growth rate of the function.

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What is the effect of decreasing the base 'b' in an exponential decay function?

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Decreasing the base 'b' (but keeping it greater than 0) results in a slower decay rate.