Suppose that the outside temperature is described by T $($t$)=$ T$0+$A sin$($wt$)).$ Set up

the differential equation for the variation of temperature inside the math building

with respect to time.

$($b$)$ Let k $=1\mathrm{.}5($hours$)1,$ T$0=60$oF$,$ A $=15$oF$,$ w $=2$$.$ Substitute these values into

your differential equation and solve.