Skills Check 5.1a: Using 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 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 a quantity increases by a constant percentage over equal time intervals, resulting in a rapid increase.

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

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Exponential decay occurs when a quantity decreases by a constant percentage over equal time intervals, resulting in a rapid decrease.

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How do you identify the growth factor in an exponential growth function?

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The growth factor is found in the equation f(x) = a(1 + r)^x, where 'r' is the growth rate expressed as a decimal.

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How do you identify the decay factor in an exponential decay function?

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The decay factor is found in the equation f(x) = a(1 - r)^x, where 'r' is the decay rate expressed as a decimal.

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What is the initial value in an exponential function?

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

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Write the equation for a population that starts at 4000 and grows at 25% per month.

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f(x) = 4000(1.25)^x.

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What is the decay factor for a car valued at $15,000 that depreciates at 8% per year?

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The decay factor is 0.92.

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If a quantity grows at a rate of 14% per week, what is the growth factor?

Back

The growth factor is 1.14.

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

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