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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 does it mean for a function to exhibit exponential growth?

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Exponential growth occurs when a quantity increases by a consistent percentage over equal time intervals, represented by a function of the form f(x) = a(b^x) where b > 1.

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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 consistent percentage over equal time intervals, represented by a function of the form f(x) = a(b^x) where 0 < b < 1.

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

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An exponential function will show a constant ratio between consecutive values, indicating that the output is multiplied by the same factor as the input increases.

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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 'a' is the initial value and 'b' is the growth factor greater than 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 'a' is the initial value and 'b' is the decay factor between 0 and 1.

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What is the significance of the base 'b' in an exponential function?

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The base 'b' determines the rate of growth or decay; if b > 1, the function represents growth, and if 0 < b < 1, it represents decay.

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How do you determine if a graph represents a linear or exponential function?

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A linear function produces a straight line, while an exponential function produces a curve that increases or decreases rapidly.

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What does the equation y = 40(1/2)^x represent?

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This equation represents an exponential decay function where the initial value is 40 and the quantity decreases by half for each unit increase in x.

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What does the equation y = 7(5/4)^x represent?

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This equation represents an exponential growth function where the initial value is 7 and the quantity increases by 25% for each unit increase in x.