Question

HALF LIFE PROBLEM

The amount of a drug in a person's bloodstream can be modeled with exponential decay. Suppose that, in 3 hours, 18% of the drug is removed from the bloodstream. What is the half-life of the drug?
A) 8.1 hours
B) 8.7 hours
C) 9.3 hours
D) 9.9 hours
E) 10.5 hours

Answer 1

i learnt abou this not to long ago but i cant remember wat my answer was but i will have a think now an if i no ill write
back :)

Answer 2

Think of the half-life (in hours) as the reciprocal (because kind of the opposite, yes?) of the number of halvings in an hour.
How many of these?
How about: a third of the number of halvings in 3 hours.
How many halvings in 3 hours?
How about: the power you need to raise a half to, so it's the same as 82%.
So you need to find the log to the base of a half of 0.82.
(And then take a third of that).

Follow?

Answer 3

(And then take the reciprocal of that.)

Answer 4

\[P _{t} = P _{0}e ^{-kt}\]
First find k using P and t given
assume P is percent of drug in bloodstream
P0 is initial condition, 100% in bloodstream
\[0.82 = e ^{-3k}\]
take ln both sides
\[k = \frac{\ln .82}{-3}\]
Now we needto solve for t when 50% of drug is in bloodstream(half-life)
\[0.5 = e ^{\frac{\ln .82}{3}t}\]
take ln of both sides
\[t = \ln .5 * \frac{3}{\ln .82} = 10.48\]