EOC Category 5 - 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 the base (a positive real number), and 'x' is the exponent.

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What is the difference between exponential growth and decay?

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Exponential growth occurs when the base 'b' is greater than 1 (b > 1), leading to an increase in value. Exponential decay occurs when the base 'b' is between 0 and 1 (0 < b < 1), leading to a decrease in value.

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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 'a', which represents the starting value when x = 0.

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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 'b' in the function f(x) = a(b^x) 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 'b' in the function f(x) = a(b^x) is between 0 and 1.

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What is the growth factor in an exponential function?

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The growth factor is the base 'b' in the function f(x) = a(b^x). It indicates how much the function increases or decreases for each unit increase in x.

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If a population doubles every day, what is the growth factor?

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The growth factor is 2, as the population multiplies by 2 each day.

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What does the term 'initial value' refer to in an exponential function?

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The initial value refers to the y-intercept of the function, which is the value of the function when x = 0.

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How can you determine which exponential function has the greatest growth?

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Compare the growth factors (the bases) of the functions. The function with the largest base will have the greatest growth.

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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.