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 it mean for an exponential function to exhibit growth?

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An exponential function exhibits growth when the base 'b' is greater than 1, resulting in the function increasing as 'x' increases.

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What does it mean for an exponential function to exhibit decay?

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An exponential function exhibits decay when the base 'b' is between 0 and 1, resulting in the function decreasing as 'x' increases.

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What is the y-intercept of an exponential function?

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The y-intercept of an exponential function f(x) = a(b)^x is the value of f(0), which equals 'a'.

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How do you identify the common ratio in an exponential function?

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The common ratio in an exponential function f(x) = a(b)^x is the base 'b'.

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What is the formula for an increasing exponential function?

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An increasing exponential function can be represented as f(x) = a(b)^x, where 'b' > 1.

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What is the formula for a decreasing exponential function?

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A decreasing exponential function can be represented as f(x) = a(b)^x, where 0 < 'b' < 1.

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How do you find the value of an exponential function at a specific point?

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To find the value of an exponential function at a specific point, substitute the value of 'x' into the function and calculate f(x).

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What is the relationship between exponential functions and their graphs?

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The graph of an exponential function is a smooth curve that either rises steeply (growth) or falls steeply (decay) as 'x' increases.

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What is the significance of the base in an exponential function?

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The base of an exponential function determines the rate of growth or decay; a larger base results in faster growth.