College Algebra & Trigonometry, 2018a

186 CHAPTER 3. EXPONENTS AND LOGARITHMS
5) A hot bowl of soup is served at a dinner party. It starts to cool according to
Newton’s Law of Cooling so that its temperature at time t is given by:
y = 65 + 145e −0.05t
where t is measured in minutes and y is measured in degrees Fahrenheit.
a) What is the initial temperature of the soup?
b) What is the temperature after 10 minutes?
c) After how long will the temperature be 100 ◦ ?
6) Newton’s Law of Cooling is used in homicide investigations to determine
the time of death. The normal body temperature is 98.6 ◦ F. Immediately following
death, the body begins to cool. This process uses Newton’s Law of Cooling:
y = T a + Ce −kt
If the ambient temperature is 60 ◦ , and the body has cooled to 72 ◦ F after 6 hours,
use this information to determine the value of k in the equation.
7) The police discover the body of a murder victim. Critical to solving the
crime is determining when the murder was committed. The coroner arrives at
the murder scene at 12 Noon. She immediately takes the temperature of the body
and finds it to be 94.6 ◦ F. She then takes the temperature 1.5 hours later and finds
it to be 93.4 ◦ F. If the temperature of the room is 70 ◦ F, when was the murder committed?