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 y = a(b^x), where 'a' is a constant, 'b' is the base (a positive number), and 'x' is the exponent.

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What does 'growth' mean in exponential functions?

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Growth in exponential functions refers to a situation where the value increases rapidly over time, typically when the base 'b' is greater than 1.

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CCSS.HSF-IF.C.8B

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What does 'decay' mean in exponential functions?

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Decay in exponential functions refers to a situation where the value decreases over time, typically when the base 'b' is between 0 and 1.

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CCSS.HSF-IF.C.8B

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What is the common ratio in an exponential sequence?

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The common ratio is the factor by which we multiply to get from one term to the next in an exponential sequence.

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CCSS.HSF.BF.A.2

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What does the 'a' represent in the equation y = a(b^x)?

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In the equation y = a(b^x), 'a' represents the initial value or the y-intercept of the function.

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CCSS.HSF.LE.B.5

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What is the base in an exponential function?

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The base is the number that is raised to a power in an exponential function, determining the rate of growth or decay.

Tags

CCSS.HSF-IF.C.8B

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How do you identify if a graph is exponential?

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A graph is exponential if it shows a curve that rises or falls sharply, rather than a straight line.

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CCSS.HSF-IF.C.7E

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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 'r' is the growth rate and 't' is time.

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CCSS.HSF-IF.C.8B

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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 'r' is the decay rate and 't' is time.

Tags

CCSS.HSF-IF.C.8B

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What is an example of an exponential growth situation?

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An example of exponential growth is population growth, where the number of individuals increases rapidly over time.

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CCSS.HSF-LE.A.1A