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 does the 'a' represent in an exponential function?

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In an exponential function, 'a' represents the y-intercept, which is the value of the function when x = 0.

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What is the difference between exponential growth and exponential decay?

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Exponential growth occurs when the base 'b' is greater than 1, leading to an increase in value as x increases. Exponential decay occurs when the base 'b' is between 0 and 1, leading to a decrease in value as x increases.

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How can you identify exponential growth on a graph?

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Exponential growth is identified on a graph by a curve that rises steeply as x increases, indicating that the function's value increases rapidly.

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How can you identify exponential decay on a graph?

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Exponential decay is identified on a graph by a curve that falls steeply as x increases, indicating that the function's value decreases rapidly.

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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.

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What is the y-intercept of the function f(x) = 3(2^x)?

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The y-intercept is 3, which is the value of the function when x = 0.

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What does the base 'b' in an exponential function determine?

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

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What is an example of an exponential growth function?

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An example of an exponential growth function is f(x) = 2(3^x), where the base 3 indicates growth.

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What is an example of an exponential decay function?

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An example of an exponential decay function is f(x) = 5(0.5^x), where the base 0.5 indicates decay.