Question

The antidepressant fluoxetine (or Prozac) has a half-life of about 3 days. What percentage of a dose remains in the body after one day? What percentage of a dose remains in the body 9 after days?

Answer 1

after 1 day percentage of dose is 79.37 %

after 9 days is 12.50 %

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

`(Q)/(2) = Q * e^(-kt)`

so as half life time 3 days

`(Q)/(2) = Q * e^(-k*3)`

so

take ln both side

`ln(1)/(2) = -3k`

k = 0.231

so it become formula

`(Q(t))/(Q)` =
`e^(-0.231*t)`

now after 1 day percentage of dose is

`(Q(1))/(Q)` =
`e^(-0.231*1)` = 0.7937 = 79.37 %

and after 9 days

`(Q(9))/(Q)` =
`e^(-0.231*9)` = 0.1250 = 12.50 %