Problem #$4$: The numerical solution may be better appreciated in situations that cannot be solved by hand. Suppose the

surrounding temperature varies with time, so that Newton's Law gives us

$T^{\text{'}}=-\frac{9}{5}[T-g(t)],T(0)=31$

at any instant of time. Adapt your code from Problem #$1$ to find $T(t)$ on the interval $0t5($NOTE: the max

time has been increased to $5$ from $3)$ for a surrounding temperature given by

$g(t)=16+10sin[\frac{10}{t^2+0\mathrm{.}5}]$

Use the number of steps you found in problem $3.$ Create a plot showing the surrounding temperature $g(t)$ as well

as the temperature $T(t)$ of the bolt, and include a legend in the lower right corner to distinguish them.

Use your First Name, Last Name, and Student Number as the title for the graph $($e$.$g$.,$ 'Johnny Good, $1234567\text{'}).$

Save the graph as a Portable Network Graphics $(.$png$)$ file, and then upload it$.$