Answer:
600 mg
Explanation:
The initial amount of the drug = 200 mg
The half-life of the drug = 8 hrs
It means that:-
After 6 hours, the concentration becomes :- [tex]\frac{200}{2}[/tex] mg
After 12 hours, the concentration becomes :- [tex]\frac{200}{4}[/tex] mg
After 18 hours, the concentration becomes :- [tex]\frac{200}{8}[/tex] mg
And so on...
Thus,
After infinite time = [tex]200+\frac{200}{2}+\frac{200}{4}+\frac{200}{8}+..[/tex]
Thus,
After infinite time = [tex]200\times (1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+..)[/tex]
The sum of the infinite series is:- [tex]1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+..[/tex] = [tex]\frac{1}{1+\frac{1}{2}}=2[/tex]
So,
After infinite time = [tex]200\times 2[/tex] mg = 600 mg
