Question

The half life of a certain tranquilizer in the bloodstream is 37 hours. How long will it take for the drug to decay to 86% of the original decay model,A=A

Answer 1

8.1 hours

Explanation:

A model of the fraction remaining can be ...

f = (1/2)^(t/37) . . . . t in hours

So, for the fraction remaining being 86%, we can solve for t using ...

0.86 = 0.5^(t/37)

log(0.86) = (t/37)log(0.5)

t = 37·log(0.86)/log(0.5) ≈ 8.0509 ≈ 8.1 . . . hours

It takes about 8.1 hours to decay to 86% of the original concentration.