ZillDIffeQ$103\mathrm{.}1\mathrm{.}022.$

The rate at which a body cools also depends on its exposed surface area $S.$ If $S$ is a constant, then a modification of the mathematical formulation of Newton's empirical law of cooling$/$warming of an object, given in this section, is

$\frac{dT}{dt}=kS(T-T_m),$

where $k<mn>0</mn>$ and $T_m$ is a constant. Suppose that two cups A and $B$ are filled with coffee at the same time. Initially, the temperature of the coffee is $145F.$ The exposed surface area of the coffee in cup $B$ is twice the surface area of the coffee in cup $A.$ After $30$ min the temperature of the coffee in cup $A$ is $95F.$ If $T_m=65F,$ then what is the temperature of the coffee in cup $B$ after $30$ min? $($Round your answer to two decimal places.$)$

$F$