6.2 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 represents growth or decay processes.

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What does the initial value in an exponential function represent?

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The initial value in an exponential function, represented by 'a' in f(x) = a * b^x, is the value of the function when x = 0.

Tags

CCSS.HSF.LE.B.5

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What is the horizontal asymptote of an exponential function?

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The horizontal asymptote of all exponential functions is the x-axis, or y = 0.

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CCSS.HSF-IF.C.7E

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How do you find the y-intercept of an exponential function?

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To find the y-intercept of an exponential function, evaluate f(0). This gives the value of the function when x = 0.

Tags

CCSS.HSF-IF.C.7E

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What is the common ratio in an exponential function?

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The common ratio in an exponential function is the factor by which the function's value changes as x increases by 1. It is represented by 'b' in f(x) = a * b^x.

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CCSS.HSF-IF.C.8B

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If f(x) = 0.05(2)^x, what is the initial value?

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The initial value is 0.05.

Tags

CCSS.HSF.LE.B.5

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If f(x) = 2 * 4^x, what is the y-intercept?

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The y-intercept is 2.

Tags

CCSS.HSF-IF.C.7E

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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.

Tags

CCSS.HSF-LE.A.1A

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How do you determine if a function is exponential?

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A function is exponential if it can be expressed in the form f(x) = a * b^x, where 'a' is a constant and 'b' is a positive real number.