Chapter 1.1, Problem 1P

Newton’s Law of Cooling. A cup of hot coffee has a temperature of ${200}^{\circ }F$ when freshly poured, and is left in a room at ${70}^{\circ }F$. One minute later the coffee has cooled to ${190}^{\circ }F$.

Assume that Newton’s law of cooling applies. Write down an initial value problem that models the temperature of the coffee.

Determine when the coffee reaches a temperature of ${170}^{\circ }F$.