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.

Question

Time, min Temperature, °F
15 2150
20 2100
30 2000
60 1700

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

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

Answer 1

since the relation is supposed to be linear, let's pick an "easy" pair, (20,2100) and (30,2000)
slope= (2100 - 2000)/(20-30)
= 100/-10 = - 10

so temp = -10t + b , where t is time in minutes
2000 = -10(30) + b

b = 2300

temp - =10t + 2300

b) for 3 hrs, temp = -10(180) + 2300
= 500