Exponential Function

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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 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, leading to rapid increases over time. The base 'b' in the function f(x) = a(b)^x is greater than 1.

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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, leading to rapid decreases over time. The base 'b' in the function f(x) = a(b)^x is between 0 and 1.

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What is the y-intercept of an exponential function?

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The y-intercept of an exponential function f(x) = a(b)^x is the value of f(0), which equals 'a'.

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What is the x-intercept of an exponential function?

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An exponential function does not have an x-intercept; it never crosses the x-axis.

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How do you determine if a graph represents growth or decay?

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If the graph rises as x increases, it represents growth. If it falls as x increases, it represents decay.

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What is the general form of an exponential growth function?

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The general form 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 is f(x) = a(b)^x, where 0 < b < 1.

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How can you write an exponential function from a table of values?

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Identify the initial value (y-intercept) and the growth/decay factor by examining the ratio of consecutive y-values.

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What is the growth factor in the function y = 6(2)^x?

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The growth factor is 2.