IXL - Exponential regression: decay (Algebra 1 practice)

A year ago, Molly bought a new laptop. This table shows the value, in dollars, of her laptop every two months since she bought it.

Molly's laptop
Months ( x )	0	2	4	6	8	10	12
Value ( y )	700	674	650	626	603	581	560

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 how much Molly's laptop will be worth 18 months after she bought it. Round your answer to the nearest dollar.

ref_doc_title.

Learn with an example

question

Tiana is learning about heat and temperature in her science class, and she decides to conduct an experiment. She puts a pot of boiling water in the freezer and measures its temperature, in degrees Fahrenheit, every 5 minutes.

Water temperature
Minutes ( x )	0	5	10	15	20
Temperature ( y )	212	180	153	130	111

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 temperature of the water 30 minutes after Tiana put it in the freezer. Round your answer to the nearest whole number.

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 temperature of the water every 5 minutes.

Water temperature
Minutes ( x )	0	5	10	15	20
Temperature ( y )	212	180	153	130	111

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

211.73

and

0.97

after rounding to the nearest hundredth.

So, this function models the data:

211.73

(

0.97

)

Now, use the function to estimate the temperature of the water 30 minutes after Tiana put it in the freezer. Substitute 30 for

211.73

(

0.97

)

211.73

(

0.97

)

84.9052…

≈

So, the function predicts the water's temperature will be about

30 minutes after Tiana put it in the freezer.

You can visualize this process by graphing the original data along with the exponential function. You can use the function to predict the water's temperature at times other than those given in the table. For example, the function predicts the water's temperature will be about

30 minutes after Tiana put it in the freezer.

$Confetti$

Excellent!

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Teacher tools

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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