Question

Q7 After a person takes medicine, the amount of drug left in the person’s body changes over time. When testing a new drug, a pharmaceutical company develops a mathematical model to quantify this relationship. To find such a model, suppose a dose of 1000 mg of a certain drug is absorbed by a person’s bloodstream. Blood samples are taken every five hours, and the amount of drug remaining in the body is calculated. The data collected from a particular sample is recorded below. What is the rate of decay of the medication?
hours since drug was taken, amount left in body
0,1000
5,550
10,316
15,180
20,85
25,56
30,31


i need the rate of decay

Answer 1

The data fit an exponential decay A(t)=A0 e^{kt}. Fitting ln(A) vs t (least-squares) gives

k ≈ -0.1164 h^(-1),

so A(t) ≈ 1000 e^{-0.1164 t}. The corresponding half-life is t1/2 = ln2/0.1164 ≈ 5.95 hours. (This is about a 11.6% continuous decay rate, i.e. ≈10.98% lost per hour multiplicatively.)