Exponential Functions Recap

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What is an exponential function?

Back

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 a function to exhibit exponential growth?

Back

A function exhibits exponential growth when the base 'b' in the function f(x) = a * b^x is greater than 1.

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CCSS.HSF-IF.C.8B

Front

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

Back

A function exhibits exponential decay when the base 'b' in the function f(x) = a * b^x is between 0 and 1.

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CCSS.HSF-IF.C.8B

Front

In the function f(x) = a * b^x, what does the variable 'a' represent?

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The variable 'a' represents the initial value or the y-intercept of the exponential function.

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CCSS.HSF.LE.B.5

Front

In the function f(x) = a * b^x, what does the variable 'b' represent?

Back

The variable 'b' represents the growth (if b > 1) or decay (if 0 < b < 1) factor of the exponential function.

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CCSS.HSF-IF.C.8B

Front

How can you determine if a function is exponential growth or decay from its equation?

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You can determine if a function is exponential growth or decay by examining the base 'b': if b > 1, it is growth; if 0 < b < 1, it is decay.

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CCSS.HSF-IF.C.8B

Front

What is the general shape of the graph of an exponential growth function?

Back

The graph of an exponential growth function rises steeply as x increases, starting from the initial value 'a'.

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CCSS.HSF-IF.C.7E

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What is the general shape of the graph of an exponential decay function?

Back

The graph of an exponential decay function decreases rapidly as x increases, approaching the x-axis but never touching it.

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CCSS.HSF-IF.C.7E

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What is the horizontal asymptote of an exponential decay function?

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The horizontal asymptote of an exponential decay function is the x-axis (y = 0), which the graph approaches but never reaches.

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CCSS.HSF-IF.C.7E

Front

What is the difference between exponential growth and linear growth?

Back

Exponential growth increases at a rate proportional to its current value, while linear growth increases by a constant amount.

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CCSS.8.F.A.2

CCSS.HSF.IF.C.9