Solve the Problem $\mathrm { U } = \mathrm { T } + \left( \mathrm { U } _ { \mathrm { O } } - \mathrm { T } \right) \mathrm { e } ^ { \mathrm { kt } }$

Essay

Solve the problem.
-The temperature (in degrees Fahrenheit) of a dead body that has been cooling in a room set at 70° is measured
as 88°. One hour later, the body temperature is 87.5°. How long (to the nearest hour) before the first
measurement was the time of death, assuming that the body temperature of the deceased at the time of death
was 98.6°. Assume the cooling follows Newton's Law of Cooling: $\mathrm { U } = \mathrm { T } + \left( \mathrm { U } _ { \mathrm { O } } - \mathrm { T } \right) \mathrm { e } ^ { \mathrm { kt } }$