Problem $2($Lake pollution$)$

Euler's Method

A polluted lake has an initial concentration of a bacteria of ${10}^{7}ppm,$ while the acceptable level is only $0\mathrm{.}5x{10}^{6}ppm.$ The concentration of the bacteria reduces over time at a rate $(R)$ of $0\mathrm{.}04pp\frac{m}{?}$ day and is also impacted as fresh water enters the lake. The differential equation that governs the concentration C of the pollutant as a function of time $($in days$)$ is given by

$\frac{dC}{dt}=-C(R+0\mathrm{.}06)$

Using Euler's method, find the concentration of the pollutant after $12$ weeks. Is the concentration of bacteria under the acceptable limit at the end of $4$ weeks? Provide appropriate plot$($s$)$ to support your results.

Hint:

For explanation about Euler's method, go through the Week $8$ Lecture Video.

Deliverables:

One completed project write$-$up per team $($the worksheet with the $5$ problem$-$solving steps$)$

The problem$-$solving steps $1-3$ for problem $1$&$2$ should be shown to your ULA at the end of Lab $7$A$.$

One MATLAB script per team showing your work with clearly labeled and commented solutions.

All submissions must be done via D$2$L drop box, which can be found in the Assessments and then Assignments. All your work is due before the beginning of Lab $8A.$