The halflife of a certain tranquilizer in the bloodstream is

The half-life of a certain tranquilizer in the bloodstream is 50 hours. How long will it take for the drug to decay to 94% of the original dosage?

Use the exponential decay model, A=A₀e^kt to solve.

Solution

Let the initial amount be 100

After t hours amount left=100-94=6

we have to use the following formula

A=A₀e^kt

6=100 e^kt

.06=e^kt

(ln.06)/t=k

half life is 50 yrs

.5=e^50k

.5=e^50(ln.06)/t

.5=.06^50/t

t=203 yrs