$($Total of $6+2$ marks$)$ A solution containing a $50mg$ per $L$ of drug is administered intravenously at a

continuous rate of $60mL$ per hour. Assume that there is no drug in the patient's body initially, and the

volume of blood in the body remains a constant $5L$ during this process. If the drug is metabolized at a

rate of $50\%$ per hour.

$($a$)(6$ marks$)$ What is the amount of drug found in a patient's body after $t$ hours? I got the DE u$\text{'}=3-($ln$2+0\mathrm{.}012)$u which i knpw is correct but i cannot solve it$,$ also need to us initla condition u$(0)=0.$

$($b$)$ Bonus $(2$ marks$)$ Write a code to plot the amount of drug in the body you found in part $($a$)$ with

respect to time on the interval $0,24.$ The code should be included as well as the plot. The curve

should be "Red" and the axis should be labelled properly.