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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 graph of an exponential growth function look like?

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The graph of an exponential growth function rises sharply as x increases, showing a rapid increase in value.

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What does the graph of an exponential decay function look like?

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The graph of an exponential decay function falls sharply as x increases, approaching zero but never touching the x-axis.

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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, which indicates how much the function increases for each unit increase in x.

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What is the decay factor in an exponential function?

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The decay factor is the base 'b' in the function f(x) = a * b^x, where 0 < b < 1, indicating how much the function decreases for each unit increase in x.

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How do you identify exponential growth from a table of values?

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Exponential growth can be identified if the ratio of consecutive outputs (y-values) is constant and greater than 1.

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How do you identify exponential decay from a table of values?

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Exponential decay can be identified if the ratio of consecutive outputs (y-values) is constant and less than 1.

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What is the difference between linear and exponential functions?

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Linear functions have a constant rate of change, while exponential functions have a variable rate of change that increases or decreases rapidly.

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What is an example of a real-world situation modeled by an exponential function?

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An example is population growth, where a population triples every year, modeled by an exponential function.

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What does it mean if a function has a negative growth factor?

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A negative growth factor indicates that the function is decreasing, which is characteristic of exponential decay.