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Homework Statement
Suppose that the human body dissipates a drug at a rate proportional to the amount y of drug present in the bloodstream at time t. At time t = 0 a first injection of Y0 grams is made into a body that was drug free prior to t = 0.
a) Amount of drug at the end of T hours.
b) If at time T a second injection of y0 is made, find the amount of drug at the end of 2T hours.
c) If at the end of each time period of length T an injection of Y0 is made, find the amount of rug at the end of n*T hours.
d) Find the limiting value of the answer to (c) as n->∞.
Homework Equations
dy/dt ∝ y(t)
y(0) = y0
The Attempt at a Solution
I'm not sure what equation would give me the model required for this question...
It appears we have logistic decay so it would be something like:
y0e-kt/(1 - e-kt)
I'd appreciate being nudged in the right direction.