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 a positive real number, and 'x' is the exponent.

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

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

Tags

CCSS.HSF-IF.C.8B

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

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Exponential decay occurs when a quantity decreases by a consistent percentage over equal intervals of time, resulting in a rapid decrease.

Tags

CCSS.HSF-IF.C.8B

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How can you identify an exponential decay function from its equation?

Back

An exponential decay function has a base 'b' that is between 0 and 1 (0 < b < 1).

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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 'a', which represents the initial value when x = 0.

Tags

CCSS.HSF-IF.C.7E

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What is the common ratio in an exponential sequence?

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The common ratio in an exponential sequence is the factor by which each term is multiplied to get the next term.

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CCSS.HSF.BF.A.2

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How do you determine if a graph represents exponential growth or decay?

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If the graph rises steeply as x increases, it represents exponential growth; if it falls steeply, it represents exponential decay.

Tags

CCSS.HSF-IF.C.7E

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What is the formula for calculating the value of an exponential function at a given x?

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The value of an exponential function at a given x is calculated using f(x) = a * b^x.

Tags

CCSS.HSF-IF.C.8B

Front

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

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The base 'b' determines the rate of growth or decay; if b > 1, the function grows; if 0 < b < 1, the function decays.

Tags

CCSS.HSF-IF.C.8B

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What is an example of an exponential growth scenario?

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An example of exponential growth is population growth, where the population increases by a percentage each year.

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CCSS.HSF-LE.A.1A