Question

The number of milligrams of a diabetic drug in a person's system after t hours is given by the function D(t)=20e^(-0.4t).how many milligrams of the drug did this patient initially take?

Answer 1

These exponential formulas for radioactive decay, drug metabolism, etc. are of the form
\(Q(t) = Q(0)e^{-kt}\) where \(Q(0)\) is the initial quantity and \(k\) is a constant that depends on the rate.

At \(t=0\), the formula becomes \[Q(t) = Q(0)e^0 = Q(0)*(1)\]so you can find the initial amount by inspection of the formula.