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.

Front

What does the base of an exponential function represent?

Back

The base of an exponential function represents the growth (if greater than 1) or decay (if between 0 and 1) factor of the function.

Tags

CCSS.HSF-IF.C.8B

Front

How do you write an exponential decay function?

Back

An exponential decay function can be written as f(x) = a(1 - r)^x, where 'r' is the decay rate.

Tags

CCSS.HSF-IF.C.8B

Front

What is the decay rate in the function y = 15,000(0.92)^x?

Back

The decay rate is 8%, as 0.92 represents a decrease of 8% from the original value.

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(1 + r)^x, then 'r' is the growth rate.

Tags

CCSS.HSF-IF.C.8B

Front

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

Back

This equation represents an exponential growth function 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 can you model a situation where a quantity is halved each time period?

Back

You can model this situation with the function y = a(0.5)^x, where 'a' is the initial quantity.

Tags

CCSS.HSF.LE.A.2

Front

What is the significance of the initial value 'a' in an exponential function?

Back

The initial value 'a' represents the starting amount or quantity before any growth or decay occurs.

Tags

CCSS.HSF-IF.C.8B

Front

In the context of depreciation, how is the decay factor calculated?

Back

The decay factor is calculated as 1 minus the depreciation rate. For an 8% depreciation rate, the decay factor is 0.92.

Tags

CCSS.HSF-IF.C.8B

Front

What does the term 'exponential growth' mean?

Back

Exponential growth refers to an increase in quantity where the rate of growth is proportional to the current amount, leading to rapid increases over time.

Tags

CCSS.HSF-IF.C.8B