Chapter 11.1, Problem 60E

Newton's Law of Cooling When a dead body is discovered, one of the first steps in the ensuing investigation is for a medical examiner to determine the time of death as closely as possible. Have you ever wondered how this is done? If the temperature of the medium (air, water, or whatever) has been fairly constant and less than 48 hours have passed since the death, Newton's law of cooling can be used. The medical examiner does not actually solve the equation for each case. Instead, a table based on the formula is consulted. Use Newton's law of cooling to work the following exercises. Source: The College Mathematics Journal.

Assume the temperature of a body at death is ${98.6}^{°}\text{F}$, the temperature of the surrounding air is ${68}^{°}\text{F}$, and at the end of one hour the body temperature is ${90}^{°}\text{F}$.

a. What is the temperature of the body after 2 hours?

b. When will the temperature of the body be ${75}^{°}\text{F}$?

c. Approximately when will the temperature of the body be within ${0.01}^{°}$ of the surrounding air?