An item costs 500 at time t 0 and costs p in year t when

Question

Question: An item costs $500 at time t = 0 and costs $P in year t. When inflation is r% per year, the price is given by

P = 500e^rt/100

(a) If r is a constant, at what rate is the price rising (in dollars per year)

(i) Initially?

(ii) After 2 years?

(b) Now suppose that r is increasing by 0.3 per year when r = 4 and t = 2. At what rate (dollars per year) is the price increasing at that time?