multiple part algebra

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 for various times (in minutes) is shown in the following table.

Time (min)Temperature (°F)
15	1950
20	1900
30	1800
60	1500

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

T(t) = 

 

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

The value of the slope means that the temperature is decreasing at a rate of  °F per minute.

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

 °F

Answer 1

Looks like it's linear. Chg in temp/time req'd has the same value in each time period.

You could plot the points with temp on the y-axis and time across the x-axis.

(1900 - 1950)/ (20 - 15) = -50/5 = -10 degrees F/min.

(1800 - 1900)/(30 - 20) = -100/10 = -10 " "

(1500 - 1800)/(60 - 30) = -300/30 = -10 " "

Overall, the temp dropped 450 degrees in 45 minutes, or 10 degrees/min.

So the slope is -10 degrees/min. (m in the slope-intercept linear formula)

y = mx + b or, in this case temp = m(time) + b. Need to find b by plugging in any pair of values:

1500 = -10(60) + b -> b = 1500 + 600 = 2100 degrees

(a) T(t) = -10t + 2100

(b) Is pretty self-explanatory.

(c) Can you substitute the appropriate value for 3 hrs for t in the equation? (Remember, t is defined in minutes)