$3$ Assignment

Find the solution $T(t)$ for the initial value problem

iemperature

given that

unknown $(solve-$integrate$)$

$T_r=70F,T_c=10F,T_0=59F,r=()-1()-1$

Note: To get credit for this assignment you need to provide the details of your work.

$2.$ Use the formula for $T(t)($it is the result of the previous step$)$ to derive the expression for the temperature $T_{}$ in the cavity when $t.$ Make sure to label axes and specify the units for both temperature and time. Use the graph to estimate how much time does it take for temperature value to reach its equilibrium value.

$3.$ Use software $($MATLAB$)$ to plot the graph of the function $T=T(t)$ on the interval $0t18$ hours. Symbolic $(240)$

$4.$ What should be $T_c$ to make $T_{}$ equal to ${32}^{0}F$ which is the freezing point for water?

$5.$ Think about the limitations of our model. Suggest how it can be improved.

Submit to the Blackboard your answers for questions $1-5.$ Your work will include a written part $($answers for questions $1,2,4,5),$ as well as the MATLAB script $(m-$file$)$ and a picture saved in $.$jpeg, $.$png$,.$pdf$,$ or $.$eps format $($for question $3).$