IXL - Exponential regression (Precalculus practice)

The highest ski lift in the northern hemisphere is the Imperial Express SuperChair in Breckenridge, Colorado. The ski lift rises to an elevation of 3,914 meters. This table shows the air pressure, measured in kilopascals, at various heights, measured in kilometers from the ski lift's base.

Ski lift
Height above the base ( x )	0.18	0.2	0.22	0.24	0.26	0.28
Air pressure ( y )	63.182	63.018	62.855	62.692	62.529	62.367

Use exponential regression to find the function that best fits the data.

Write your answer in the form

(

)

Round

and

to the nearest hundredth.

Use the exponential function to estimate the air pressure at the base of the chairlift. Round your answer to the nearest hundredth.

kilopascals

ref_doc_title.

Learn with an example

question

Dan has a large red maple tree in his front yard. Every fall, the leaves change color and fall off the tree. This table shows the approximate number of leaves, in thousands, on the tree since they began falling.

Red maple leaves
Days ( x )	0	5	10	15	20	25
Leaves ( y )	60	51.5	44.2	38	32.6	28

Use exponential regression to find the function that best fits the data.

Write your answer in the form

(

)

Round

and

to the nearest hundredth.

Use the exponential function to estimate the number of leaves on the tree 30 days after they began falling. Round your answer to the nearest thousand leaves.

thousand leaves

key idea

If you have a set of data, you can try to model it with a function. One way to do this is with exponential

regression,

which gives the exponential function that best fits the data. Exponential regression is a good choice when the data roughly follows an exponential pattern.

solution

This table shows the approximate number of leaves, in thousands, on the tree since they began falling.

Red maple leaves
Days ( x )	0	5	10	15	20	25
Leaves ( y )	60	51.5	44.2	38	32.6	28

Use exponential regression to fit a function of the form

(

)

to the data. You can do this with a calculator or a computer. Your answers may vary depending on which tool you use.

Enter the first row in the table for the

-values,

and enter the second row for the

-values.

Depending on which tool you use, you should find that

59.99

and

0.97

after rounding to the nearest hundredth.

So, this function models the data:

59.99

(

0.97

)

Now, use the function to estimate the number of leaves on the tree 30 days after they began falling. Substitute 30 for

59.99

(

0.97

)

59.99

(

0.97

)

24.0564…

≈

So, the function estimates there will be about 24 thousand leaves on the tree 30 days after they began falling.

You can visualize this process by graphing the original data along with the exponential function. You can use the function to estimate the number of leaves on the tree at times other than those given in the table. For example, the function estimates there will be about 24 thousand leaves on the tree 30 days after they began falling.

Looking for more? Try this:

$Confetti$

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Not feeling ready yet? These can help:

Z.2Evaluate exponential functions

H.5Describe linear and exponential growth and decay

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