Writing Exponential Functions from Word Problems

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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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How do you identify exponential growth?

Back

Exponential growth occurs when the base 'b' in the function f(x) = a(b)^x is greater than 1.

Tags

CCSS.HSF-IF.C.8B

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How do you identify exponential decay?

Back

Exponential decay occurs when the base 'b' in the function f(x) = a(b)^x is between 0 and 1.

Tags

CCSS.HSF-IF.C.8B

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What does the initial value in an exponential function represent?

Back

The initial value is the value of the function when x = 0, represented by 'a' in the function f(x) = a(b)^x.

Tags

CCSS.HSF.LE.B.5

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In the function f(h) = 6(3)^h, what does '6' represent?

Back

The '6' represents the initial number of cells present before any growth occurs.

Tags

CCSS.HSF.LE.B.5

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What does the term 'rate of growth' mean in an exponential function?

Back

The rate of growth is the percentage increase applied to the initial value in an exponential growth function.

Tags

CCSS.HSF-IF.C.8B

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What does the term 'rate of decay' mean in an exponential function?

Back

The rate of decay is the percentage decrease applied to the initial value in an exponential decay function.

Tags

CCSS.HSF-IF.C.8B

Front

Write an exponential function for a quantity that triples every hour starting from 10.

Back

f(h) = 10(3)^h.

Tags

CCSS.HSF.LE.A.2

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If a function is modeled by f(x) = 200(0.9)^x, what does 0.9 represent?

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0.9 represents a 10% decay rate.

Tags

CCSS.HSF.LE.B.5

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How do you convert a percentage growth rate to a base for an exponential function?

Back

To convert a percentage growth rate 'r' to a base, use the formula b = 1 + r (as a decimal). For example, a 6% growth rate becomes b = 1 + 0.06 = 1.06.

Tags

CCSS.HSF.LE.A.2