Answer:
after 1 day percentage of dose is 79.37 %
after 9 days is 12.50 %
Step-by-step explanation:
given data
half-life = 3 days
to find out
What percentage of a dose remains in the body after one day and after 9 days
solution
we know the half lie Prozac formula that is
[tex]\frac{Q}{2} = Q * e^{-kt}[/tex]
so as half life time 3 days
[tex]\frac{Q}{2} = Q * e^{-k*3}[/tex]
so
take ln both side
[tex]ln\frac{1}{2} = -3k[/tex]
k = 0.231
so it become formula
[tex]\frac{Q(t)}{Q}[/tex] = [tex]e^{-0.231*t}[/tex]
now after 1 day percentage of dose is
[tex]\frac{Q(1)}{Q}[/tex] = [tex]e^{-0.231*1}[/tex] = 0.7937 = 79.37 %
and after 9 days
[tex]\frac{Q(9)}{Q}[/tex] = [tex]e^{-0.231*9}[/tex] = 0.1250 = 12.50 %
