# exponential decay

• Jul 22nd 2010, 11:54 PM
Wullz16
exponential decay
A dosage of Q units of a certain drug is administered daily to a patient. If the amount of the drug in the bloodstream after n days is given by Qe^-kn where k is a constant, find:

(i) The value of k if the amount of drug found in the bloodstream has halved after 1 day prior to administering the second dosage. Express your answer to three decimal places.

(ii) Hence find the amount of drug found in the bloodstream after 15 days, prior to administering the next dosage

Teacher said something about this question following simmilar to a supperannuation process but i don't understand. I need help with both parts.
• Jul 23rd 2010, 12:03 AM
pickslides
Quote:

Originally Posted by Wullz16

(i) The value of k if the amount of drug found in the bloodstream has halved after 1 day prior to administering the second dosage. Express your answer to three decimal places.

$Q=Q_0e^{-kn}$

From the information given

$\frac{Q_0}{2}=Q_0e^{-k\times 1}$

$\frac{1}{2}=e^{-k}$

$\ln\frac{1}{2}=-k$

$k = -\ln\frac{1}{2}$

Quote:

Originally Posted by Wullz16
(ii) Hence find the amount of drug found in the bloodstream after 15 days, prior to administering the next dosage

Sub in k as found above into $Q=Q_0e^{-k\times 1}$ and solve for Q when n=15.