A drug is eliminated from the body through the kidney in such a way that over each hour, 25% of the amount present at the beginning of the hour is eliminated. Let t be the amount of time (in hours) since the drug was first taken, and A0 the initial amount of the drug in the body.

Question

A(t) = A0e^(kt)

k is some constant. How long does it take before the amount of drug in the body is half of the initial amount?

Answer 1

A(t) = A0 (0.75)^t = A0 (e^ln(0.75))^t = A0 e^(ln(0.7t) t)
so, k = ln(0.75)

now you can find when A(t) = 0.5 A0