If the half life of a drug in the bloodstream is 15 hours ho

If the half life of a drug in the bloodstream is 15 hours, how much drug is left in the bloodstream 36 hours after a 400 miligram dose?

Solution

Given that half life = 15 hours

i.e. P(15) = P0/2 = P0e^-15k

We can find K using this

e^-15k = 0.5

-15k = -0.6931

k =0.0462

Hence equation is

P(t) = P0e^-0.0462t

where t is the hours

If P0 = 400, and (t) =36

then P(36) = 400e^-0.0462(36)

= 73.034 mg.