Newton's Law of Cooling might seem unneccesary at first- why would you want to know how quickly salt water cools? Still, it has an interesting application in real life.

Forensics experts use Newton's Law of Cooling to find out when victims of crimes died. They take the temperature of the body when they find it, and by knowing that the average temperature of the human body is 98.6 degrees initially (assuming the dead person wasn't sick!) and measuring the room temperature, they can find k and then find t.

Here's an example problem of this:

Suppose that a corpse was discovered in a motel room at midnight and its temperature was . The temperature of the room is kept constant at . Two hours later the temperature of the corpse dropped to . Find the time of death.

Solution: First we use the observed temperatures of the corpse to find the constant k. We have

.

In order to find the time of death we need to remember that the temperature of a corpse at time of death is (assuming the dead person was not sick!). Then we have

which means that the death happened around 7:26 P.M.