Question

A piece of pottery is removed from a kiln and allowed to cool in a controlled environment. The temperature (in degrees Fahrenheit) of the pottery after it is removed from the kiln is shown for various times (in minutes) in the following table.

Time(min) Temperature (F)
15 2200
20 2150
30 2050
60 1750

a.) Find a linear model for the temperature of the pottery after t minutes

b.) Explain the meaning of the slope of this line in the context of the problem.

c.) Assuming that the temperature continues to decrease at the same rate, what will be the temperature of the pottery in 3 hours?

Answer 1

You are given the XY coordinates. Take Time to be X, and Temperature to be Y. Create a graph on a Cartesian coordinate system.
A) If done correctly your linear Regression should be Y=-10X + 2350.

B) Your slope is -10. Meaning that for every 1 minute the pottery cools by 10 degrees.

C) From B we can see that the temperature will continue to cool 10 degrees every minute. There are 60 minutes in an hour X two hours gives us 120 minutes. Multiply that 120 minutes by -10 degrees per minute. And you get -1200 degrees. You then add this to your final temperature at the one hour mark to get a final temperature at three hours as 550 degrees F.