(Solved): The rate of change of temperature of an object is proportional to the difference in temperature ...

The rate of change of temperature of an object is proportional to the difference in temperature between the object and its surroundings $\frac{dT}{dt}=-k\left(T-T_s\right)$ where $T(t)$ is the temperature of the object at time $t$ and $T_s$ is the temperature of the surroundings, sometimes called the ambient temperature. The temperature can be found using separable method as $T(t)=T_s+A{e}^{kt}$. Problem: A cup of coffee is made with boiling water at a temperature of $100^{\circ }\mathrm{C}$, in a room at temperature $20^{\circ }\mathrm{C}$. After two minutes it has cooled to $80^{\circ }\mathrm{C}$. What is $T_s$ ? What is $A$ ? What is $k$ ? (Give your answer to 2 decimal places.)