Question: CRUISE SHIP BOOKINGS The management of Cruise World, operators of Caribbean luxury cruises, expects that the percentage of young adults booking passage on their cruises in the years ahead will rise dramatically. They have constructed the following model, which gives the percentage of young adult passengers in year t:
p = f(t) = 50(t2 + 2t + 4) (0 ≤ t ≤ 5)
(t2 + 4t + 8)
Young adults normally pick shorter cruises and generally spend less on their passage. The following model gives an approximation of the average amount of money R (in dollars) spent per passenger on a cruise when the percentage of young adults is p:
R(p) = 1000(p + 4)
(p + 2)
Find the rate at which the price of the average passage will be changing 2 yr from now.