An importer of Brazilian coffee estimates that local consume

An importer of Brazilian coffee estimates that local consumers will buy approximately Q (p) = 4374/p^2 kilograms of the coffee per week when the price is p dollars per kilogram. It is estimated that t weeks from now the price of this coffee will be p (t) = 0.04t^2 + 0.2t + 12 dollars per kilogram. Express the weekly demand (kilograms sold) for the coffee as a function of t. Q(p(t)) = How many kilograms of the coffee will consumers be buying from the importer 10 weeks from now? Q (10) = When will the demand for the coffee be 30.375 kilograms? 30.375 =

Solution

Q(p)=4374/p²

p(t)=0.04t²+0.2t+12

Q(p(t))=Q(0.04t²+.2t+12)=4374/(0.04t²+0.2t+12)

b. Q(10)= 4374/(0.04(100)+0.2(10)+12) = 4374/18=243kgs