A model of tumour growth under chemotherapy from time t = 0 to t = t₁ > 0 is dC C = -C log - dt Стах DC 1+ D (*) where, at time t, C(t) is the size of the tumour, Cmax > 0 is the maximum size of the tumour, a constant, so that 0 < C(t) ≤ Cmax, and D(t) > 0 is the rate at which the drug is administered. Show that by making the change of variable, x = log(C/Cmax), equation (*) becomes D dx = -x dt 1+ D' where -00 < x < 0. = It is required to reduce the size of the tumour from Co at t = 0 to C₁ at t = t1. Let x0 = log(Co/Cmax) and x1 log(C₁/Cmax). For the health of the patient, it is desired to minimise the total amount of drug administered, which is given by the functional rt1 S[D] = = √ dt D(t).