Question

The? half-life of a certain tranquilizer in the bloodstream is 4242 hours. how long will it take for the drug to decay to 8686?% of the original? dosage? use the exponential decay? model, upper a equals upper a 0 e superscript kta=a0ekt?, to solve.

Answer 1

For this problem, we use the formula for radioactive decay which is expressed as follows:

An = Aoe^-kt

where An is the amount left after time t, Ao is the initial amount and k is a constant. 

We calculate as follows:

An = Aoe^-kt
0.5 = e^-k(42 hrs)
k = 0.0165 / hr

An = Aoe^-kt
.86 =e^-0.0165(t)
t = 9.14 hrs