## anonymous 5 years ago 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

1. anonymous

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 :)

2. anonymous

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?

3. anonymous

(And then take the reciprocal of that.)

4. anonymous

$P _{t} = P _{0}e ^{-kt}$ 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 $t = \ln .5 * \frac{3}{\ln .82} = 10.48$