After injection of a dose D of insulin, the concentration of insulin in a patient's system decays exponentially and so it can be written as De^(-at) where t respresents time in hours and a is a positive constant.

a) If a dose D is injected every T hours, write an expresssion of the sum of the residual concentrations just before the (n+1)st injection.

b) Determine the limiting pre-injection concentration.

c) If the concentration of insulin must always remain at or above a critical value C, determine the minimal dosage D in terms of C,a, and T.