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 the base 'b' in an exponential function represent?

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The base 'b' represents the growth factor if b > 1 (exponential growth) or the decay factor if 0 < b < 1 (exponential decay).

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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 point where the graph intersects the y-axis, which occurs at (0, a) where 'a' is the initial value.

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What is the x-intercept of an exponential function?

Back

An exponential function does not have an x-intercept because it never touches the x-axis; it approaches it asymptotically.

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What is an asymptote in the context of exponential functions?

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An asymptote is a horizontal line that the graph of the function approaches but never touches, typically the line y = 0 for exponential functions.

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What does the 'a' represent in the exponential function f(x) = a * b^x?

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The 'a' represents the initial value or y-intercept of the function.

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What is exponential growth?

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Exponential growth occurs when the growth rate of a value is proportional to its current value, leading to rapid increases over time.

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What is exponential decay?

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Exponential decay occurs when a quantity decreases at a rate proportional to its current value, leading to a rapid decrease over time.

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How can you identify exponential growth on a graph?

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Exponential growth is identified by a curve that rises steeply to the right, indicating that the function's values increase rapidly.

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How can you identify exponential decay on a graph?

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Exponential decay is identified by a curve that falls steeply to the right, indicating that the function's values decrease rapidly.