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 exponential growth mean?

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Exponential growth occurs when a quantity increases by a consistent percentage over a period of time, resulting in a rapid increase.

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What does exponential decay mean?

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Exponential decay occurs when a quantity decreases by a consistent percentage over a period of time, leading to a rapid decrease.

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What is the base in an exponential function?

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The base is the constant 'b' in the function f(x) = a(b)^x, which determines the rate of growth or decay.

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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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How do you identify exponential growth from a graph?

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

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How do you identify exponential decay from a graph?

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

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What is the common ratio in an exponential function?

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The common ratio is the factor by which the function's value multiplies for each unit increase in x, represented by the base 'b'.

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What is the formula for exponential growth?

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The formula for exponential growth is f(x) = a(1 + r)^x, where 'r' is the growth rate.

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What is the formula for exponential decay?

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The formula for exponential decay is f(x) = a(1 - r)^x, where 'r' is the decay rate.