Let y(t) be the drug concentration (in micrograms per kilogram) in a patient’s body at time t. The initial concentration is y(0) = L. Additional doses that increase the concentration by an amount d are administered at regular time intervals of length T. In between doses, y(t) decays exponentially—that is, y' = −ky. Find the value of T (in terms of k and d) for which the concentration varies between L and L − d as in Figure 12.

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L L-d y (mcg/mL) Exponential decay T Dose administered 2T 3T