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 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 is equal to 'a' in the function f(x) = a * b^x.

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What does it mean for a function to exhibit exponential growth?

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Exponential growth occurs when the base 'b' in the function f(x) = a * b^x is greater than 1, resulting in the function increasing rapidly as x increases.

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

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Exponential decay occurs when the base 'b' in the function f(x) = a * b^x is between 0 and 1, resulting in the function decreasing rapidly as x increases.

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How do you determine if a function is exponential growth or decay?

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To determine if a function is exponential growth or decay, check the base 'b': if b > 1, it's growth; if 0 < b < 1, it's decay.

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What is the initial amount in the function y = (6)^x?

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The initial amount is 1, which is the value of the function when x = 0.

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What is the general form of an exponential decay function?

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The general form of an exponential decay function is f(x) = a * b^x, where 0 < b < 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 the formula for calculating the y-intercept of an exponential function?

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The y-intercept can be calculated by evaluating the function at x = 0: f(0) = a * b^0 = a.

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What does the term 'asymptote' refer to in exponential functions?

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An asymptote is a line that a graph approaches but never touches; for exponential decay, the x-axis (y=0) is a horizontal asymptote.