Question: An importer from Brazilian coffee estimates that local consumers will buy approximately

\[Q\left( p \right)=\frac{4,374}{{{p}^{2}}}\]

kilograms of coffee per week when the price is p dollar per kilogram. It is estimated that t weeks from now the price of coffee will be

\[p\left( t \right)=0.04{{t}^{2}}+0.2t+12\]

(a) Express the weekly demand for coffee as a function of t.

(b) How many kilograms of the coffee will consumers be buying from the importer 10 weeks from now

(c) When will the demand for the coffee be 30.375 kilograms?