IXL - Exponential regression (Algebra 1 practice)

A seafood restaurant called What A Catch recently reopened under new management. This table shows the restaurant's profit, in dollars, every few days since its reopening.

Daily profit
Days ( x )	4	8	12	16	20	24
Profit ( y )	1,134	1,180	1,228	1,278	1,330	1,384

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 predict the restaurant's daily profit 28 days after it reopened. Round your answer to the nearest dollar.

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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:

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Work it out

Not feeling ready yet? These can help:

V.1Evaluate an exponential function

V.8Write exponential functions: word problems

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