Question: Fifty milligrams of a drug was injected into a patient at 6am. The drug is known to be eliminated according to the law of exponential decay. At 8.30am it was determined that 60% of the drug remained in the body. How many milligrams will remain in the body at midday?

Casey,

You are told that the drug is eliminated according to the law of exponential decay so you know the form of the function, but first you need some notation. Let t be the time in hours and say t = 0 at 6am. Let D(t) be the amount of the drug, in milligrams, remaining in the body at time t. Then you know that

D(t) = A e^-kt

where A and k are constants.

You are asked to find the value of D(t) at noon that is at t = 6 hours. To do this you need to determine the values of A and k. You know two facts

At 6am the amount of drug in the body is 50 milligrams,
that is D(0) = 50

At 8am the amount of drug in the body is 60% of 50 milligrams,
that is D(2) = 0.60 50

Use these facts to evaluate A and k and then find D(6).

Penny