A company sells a product whose demand D (in units) depends on its market price p (in rupees) as
D(p)=1200−15p.
The price itself is adjusted over time t (in months) according to the inflation model
p(t)=20e0.03t.
The monthly revenue is R(t)=p(t)D(p(t)).
(i) Express R explicitly as a function of t.
(ii) Derive a simplified formula for dtdR.
(iii) Calculate dtdR at t=12 months, correct to the nearest rupee per month.
(iv) Find the percentage rate of change of revenue at t=12 months and comment on whether the revenue is increasing or decreasing at that time.