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.

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