Exponential Functions

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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 a positive real number, and 'x' is the exponent. It describes growth or decay processes.

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What does the base of an exponential function indicate?

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The base of an exponential function indicates the growth or decay factor. If the base is greater than 1, the function represents exponential growth; if the base is between 0 and 1, it represents exponential decay.

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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 y = a(b^x), where 'a' is the initial value and 'b' is the growth factor (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 y = a(b^x), where 'a' is the initial value and 'b' is the decay factor (0 < b < 1).

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How do you determine the end behavior of an exponential function as x approaches infinity?

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For an exponential growth function, as x approaches infinity, y approaches infinity. For an exponential decay function, as x approaches infinity, y approaches zero.

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What does the y-intercept of an exponential function represent?

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The y-intercept of an exponential function represents the initial value of the function when x = 0.

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How can you find an ordered pair from an exponential function?

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To find an ordered pair, substitute a value for x into the function and calculate the corresponding y value. The ordered pair is (x, y).

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What does a factor greater than one in an exponential function indicate?

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A factor greater than one in an exponential function indicates that the function models exponential growth.

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What does a factor less than one in an exponential function indicate?

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A factor less than one in an exponential function indicates that the function models exponential decay.

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In the equation y = 200(1.08)^x, what does the 1.08 represent?

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In the equation y = 200(1.08)^x, the 1.08 represents a growth rate of 8% per time period.