Draw the plots of all the problems using function M$-$file. use matlab code

Problem $1$:

Metals are often treated to make them stronger and therefore wear longer. One problem with making a strong piece of metal is that it becomes difficult to form it into a desired shape. A strategy that gets around this problem is to form a soft metal into the shape you desire and then harden the surface. This makes the metal wear well without making it brittle.

A common hardening process is called carburizing. The metal part is exposed to carbon, which diffuses into the part, making it harder. This is a very slow process if

performed at low temperatures, but it can be accelerated by heating the part. The diffusivity is a measure of how fast diffusion occurs and can be modeled as

$D=D_0$exp$(\frac{-Q}{RT})$

where

$D=$ diffusivity, $c\frac{m^2}{s}$

$D_0=$ diffusion coefficient, $c\frac{m^2}{s}$

$Q=$ activation energy,$\frac{J}{m}o{l}^2,8\mathrm{.}314\frac{J}{m}$olK

$R=$ ideal gas constant,$\frac{J}{m}$olK

$T=$ temperature, $K.$

As iron is heated, it changes structure and its diffusion characteristics change. The values of $D_0$ and $Q$ are shown in the following table for carbon diffusing through each of iron's structures:

$\backslash$table$[[$Type of Metal,$D_0(c\frac{m^2}{s}),Q(\frac{J}{m}$olK$)$