AFDA - 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 y = a(b)^x, where 'a' is a constant, 'b' is the base (a positive real number), and 'x' is the exponent. It shows rapid growth or decay.

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What does the base of an exponential function represent?

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

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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 y = a(1 + r)^x, where 'a' is the initial amount, 'r' is the growth rate, and 'x' is the time period.

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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 y = a(1 - r)^x, where 'a' is the initial amount, 'r' is the decay rate, and 'x' is the time period.

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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 of the function is greater than 1 (e.g., y = a(1 + r)^x).

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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 of the function is between 0 and 1 (e.g., y = a(1 - r)^x).

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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 approaches the x-axis but never touches it.

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What is the y-intercept of an exponential function?

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The y-intercept of an exponential function is the value of 'y' when 'x' is 0, which is equal to 'a' (the initial amount).

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What happens to the value of an exponential function as x approaches infinity?

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As x approaches infinity, the value of an exponential growth function increases without bound, while an exponential decay function approaches zero.

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What is the effect of increasing the growth rate in an exponential function?

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Increasing the growth rate in an exponential function results in a steeper curve, indicating faster growth.