Question

After injection of a dose ? of insulin, the concentration of insulin in a patient's system decays exponentially and so it can be written as ??−??, where ? represents time in hours and ? is a positive constant. This represents the residual concentration (remaining in the patient) ? hours after injection.

(a) If a dose ? is injected every ? hours, write an expression for the sum of the residual concentrations just before the (?+1)st injection.

(b) Determine the pre-injection concentration in the long run (as the number of doses increases indefinitely.)

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

Answer 1