Newton’s law of cooling says that a hot object cools rapidly when the difference between its temperature and that of the surrounding air is large, but it cools more slowly when the object nears room temperature. Suppose a piece of aluminum is removed from an oven and left to cool. The following table gives the temperature A = A(t), in degrees Fahrenheit, of the aluminum t minutes after it is removed from the oven.
a. Explain the meaning of A(75) and estimate its
value.
b. Find the average decrease per minute of temperature during the first half-hour of cooling.
c. Find the average decrease per minute of temperature during the first half of the second hour of
cooling.
d. Explain how parts b and c support Newton’s law
of cooling.
e. Use functional notation to express the temperature of the aluminum after 1 hour and 13
minutes. Estimate the temperature at that time.
(Note: Your work in part c should be helpful.)
f. What is the temperature of the oven? Express
your answer using functional notation, and give
its value.
g. Explain why you would expect the function A
to have a limiting value.
h. What is room temperature? Explain your reasoning.