Introduction to 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 general form of an exponential function?

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The general form of an exponential function is f(x) = a * b^x, where 'a' is the initial value, 'b' is the growth factor, and 'x' is the exponent.

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How does an exponential function differ from a linear function?

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An exponential function grows by a constant factor (multiplication) for each unit increase in x, while a linear function grows by a constant amount (addition).

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What does it mean for a function to triple every day?

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It means that the function is exponential, specifically of the form f(x) = initial amount * 3^x, where the initial amount is multiplied by 3 for each day.

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CCSS.HSF.LE.A.2

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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 determines how much the function increases for each unit increase in x.

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CCSS.HSF-IF.C.8B

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What type of function is represented by a constant addition of values?

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A linear function.

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CCSS.HSF.LE.A.2

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If a function doubles every time, what type of function is it?

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It is an exponential function.

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What is the value of f(0) in the exponential function f(x) = 2^x?

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f(0) = 2^0 = 1.

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CCSS.HSF.IF.A.1

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What does the graph of an exponential function look like?

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The graph of an exponential function rises rapidly and has a characteristic curve that increases steeply as x increases.

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CCSS.HSF-IF.C.7E

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What is the y-intercept of an exponential function?

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The y-intercept 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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CCSS.HSF-IF.C.7E