Math  /  Calculus

QuestionSuppose that the human body dissipates a drug at a rate proportional to the amount yy of drug present in the bloodstream at time f. At time f=0\mathrm{f}=0 a first injection of yo\mathrm{y}_{\mathrm{o}} grams of the drug is made into a body that was free from that drug prior to that time. Find the amount of residual drug in the bloodstream at the end of T hours.

Studdy Solution
Calculate the amount of drug remaining after T T hours by substituting t=T t = T into the solution:
y(T)=y0ekT y(T) = y_0 e^{-kT}
The amount of residual drug in the bloodstream at the end of T T hours is:
y0ekT \boxed{y_0 e^{-kT}}

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