Expert: Abe Mantell - 12/29/2010

Question
Where e = the number e

F = 5e^-.04h can be used to find the number of milligrams F of a certain drug that is in a patient's bloodstream h hours after the drug was administered. When the number of milligrams reaches 2, the drug is to be administered again. What is the time between injections?

Here what I've got:

F = 5e^-0.4h
2 = 5e^-0.4h
-.04h = log5e of 2
-0.4h = .266
h = -.655

I know that the answer shouldn't be negative and should be larger. My textbook gives 2.29 (2 hours & 17 min.) as the answer. Where am I going wrong? Thanks.

Answer
What is your 3rd step: -.04h = log5e of 2 ???
It should be: ln(2)=ln(5e^-0.4h)
and then: ln(2)=ln(5)+ln(e^-0.4h)
==> ln(2)-ln(5)=-0.4h
So, h=[ln(2)-ln(5)]/-0.4 which is about 2.2907

It would be a little easier to first divide by 5, to obtain:
2/5=e^-0.4h....then you'd get: h=ln(2/5)/-0.4

OK?

Abe