The half-life of a certain tranquilizer in the bloodstream is 5050 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.

Using the exponential decay model; we calculate "k"

We know that "A" is half of A0

A = A0 e^ (k * 5050)

A/A0 = e^ (5050k)

0.5 = e^ (5055k)

In (0.5) = 5055k

-0.69315 = 5055k

k = - 0.0001371

To calculate how long it will take to decay to 86% of the original mass

0.86 = e^ (-0.0001371t)

In (0.86) = - 0.0001371t

-0.150823 = - 0.0001371 t

t = 1100 hours