The rate $at$ which a body cools also depends $on$ its exposed surface area $S.IfSis$ a constant, then a modification $of$ the mathematical formulation $of$ Newton's empirical law $of$ coolin$\frac{g}{w}$arming $ofan$

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 $is140F.$ The exposed surface area $of$ the coffee $in$

cup $Bis$ twice the surface area $of$ the coffee $in$ cup $A.$ After $30$ min the temperature $of$ the coffee $in$ cup $Ais90F.If{T}_m=60F,$ then what $is$ the temperature $of$ the coffee $in$ cup $B$ after $30$ min $?$

$(Round$ your answer $to$ two decimal places.$)$