Please use MATLAB and MATLAB alone and you can use the student id in the example thank you do much and have a nice day importantly please dont use chatgpt its nit correct QUESTION $2.$ Submit all steps, code, script, solutions, plots, etc. $[$Mark: $3\mathrm{.}5]$

Newton's Law of Cooling

Newton's law of cooling says that the temperature of a body changes at a rate proportional to the difference between its temperature and that of its surrounding medium,

$\frac{dT}{dt}=-k(T-T_{})$

where $T=$ temperature of the body in $C,t=$ time in hours, $K=$ proportionality constant in $s^{-1},T_{}=$ surrounding temperature in $C.$

To create a chalice, a piece of alloy is heated up to $1000C$ and then cooled in a pool of water to $7{}_1{}_{2}C$ before forging. The artist blacksmith repeats this process until a beautiful goblet is produced. Estimate the time it takes for the $1000C$ alloy to be immersed in the pool of water at $25C$ using Euler method. Invoke Newton's law of cooling, assuming $k=0\mathrm{.}0{}_3{s}^{-1}$ and $t=10s,1s.$

Here, ${}_1,{}_2,{}_3$ are the smallest, second smallest, and third smallest non$-$zero digits, respectively, of your student ID$.$ E$.$g$.,$ ID $=110985247$ gives ${}_1=1,{}_2=2,$ and ${}_3=4,$ i$.$e$.,$ the alloy is to be cooled to $712C,k=0\mathrm{.}04s^{-1}.$

Euler's Method

New value $=$ Old value $+$ Slope $$ Step size