Question

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.

Answer 1

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