Answer
$U(30)=45.52$ degrees F the temperature will be after $30$ minutes
$t=28.8$ minutes will it take to reach $45$ degrees F
Work Step by Step
$U(t)=T+(U_0-T)e^{kt},$
$T=70, U_0=28,$
$U(10)=70+(28-70)e^{-10k}=35,$
$70-42e^{-10k}=35,$
$42e^{-10k}=35,$
$e^{-10k}=0.833,$
$-10k=\ln{0.833},$
$k=-0.018,$
-$U(30)=70-42e^{-0.54},$
$=45.52$ degrees F the temperature will be after $30$ minutes
-$U(t)=70+(28-70)e^{-0.018t}=45,$
$-42e^{-0.018t}=-25,$
$e^{-0.018t}=0.5952,$
$-0.018t=\ln{0.5952},$
$t=28.8$ minutes will it take to reach $45$ degrees F
