Writing Exponential Functions

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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 the base of an exponential function represent?

Back

The base of an exponential function represents the growth or decay factor. If the base is greater than 1, it indicates growth; if it is between 0 and 1, it indicates decay.

Tags

CCSS.HSF-IF.C.8B

Front

How do you write an exponential function for depreciation?

Back

To write an exponential function for depreciation, use the formula V(t) = V_0 * (1 - r)^t, where V_0 is the initial value, r is the rate of depreciation, and t is time.

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What is the decay factor in an exponential decay function?

Back

The decay factor is calculated as (1 - r), where r is the rate of decay. It represents the fraction of the value that remains after each time period.

Tags

CCSS.HSF-IF.C.8B

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Write an exponential function for a car that depreciates at 12% per year starting from $18,000.

Back

V(t) = 18000(0.88)^t.

Tags

CCSS.HSF.LE.A.2

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What does the equation f(x) = 300(1.06)^x represent?

Back

This equation represents an exponential growth model where the initial amount is $300 and it grows at a rate of 6% per time period.

Tags

CCSS.HSF-IF.C.8B

Front

How do you determine the growth rate from an exponential function?

Back

The growth rate can be determined from the base of the function. If the function is in the form f(x) = a(b)^x, the growth rate is (b - 1) * 100%.

Tags

CCSS.HSF-IF.C.8B

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What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when the base of the function is greater than 1, leading to an increase over time. Exponential decay occurs when the base is between 0 and 1, leading to a decrease over time.

Tags

CCSS.HSF-IF.C.8B

Front

Write an equation for a culture of bacteria that starts with 5000 cells and dies by 30% each year.

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y = 5000(0.7)^t.

Tags

CCSS.HSF.LE.A.2

Front

What does a base of 1.06 in an exponential function indicate?

Back

A base of 1.06 indicates a growth rate of 6%.

Tags

CCSS.HSF-IF.C.8B