Graph 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 y-intercept of an exponential function?

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The y-intercept of an exponential function is the value of the function when x = 0, which represents the initial amount before growth or decay begins.

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How do 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 do 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 formula for exponential growth?

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The formula for exponential growth is y = a(1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate, and 't' is time.

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What is the formula for exponential decay?

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The formula for exponential decay is y = a(1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is time.

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

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

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What is the significance of the constant 'a' in an exponential function?

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The constant 'a' represents the initial value or starting amount of the quantity being modeled by the exponential function.