IXL - Exponential regression (Algebra 2 practice)

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

ref_doc_title.

Learn with an example

question

Brad is hiking to the top of Mt. Elbert, which is the highest mountain in Colorado. He records the air pressure, in atmospheres, at various altitudes, in thousands of feet.

Brad's hike
Altitude, in thousands of feet ( x )	10.5	11	11.5	12	12.5	13	13.5
Air pressure ( y )	0.67	0.66	0.65	0.64	0.62	0.61	0.60

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 summit of Mt. Elbert, which is at 14.4 thousand feet. Round your answer to the nearest hundredth.

atmospheres

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 air pressure, in atmospheres, at various altitudes, in thousands of feet.

Brad's hike
Altitude, in thousands of feet ( x )	10.5	11	11.5	12	12.5	13	13.5
Air pressure ( y )	0.67	0.66	0.65	0.64	0.62	0.61	0.60

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

1.01

and

0.96

after rounding to the nearest hundredth.

So, this function models the data:

1.01

(

0.96

)

Now, use the function to estimate the air pressure at the summit of Mt. Elbert, which is at 14.4 thousand feet. Substitute 14.4 for

1.01

(

0.96

)

1.01

(

0.96

)

14.4

0.5610…

≈

0.56

So, the function estimates the air pressure will be about 0.56 atmospheres at the summit.

You can visualize this process by graphing the original data along with the exponential function. You can use the function to estimate the air pressure at altitudes other than those given in the table. For example, the function estimates the air pressure will be about 0.56 atmospheres at 14.4 thousand feet.

Looking for more? Try this:

$Confetti$

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Z.2Evaluate exponential functions

Z.3Write exponential functions: word problems

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