Question: CONSUMER DEMAND An importer of Brazilian coffee estimates that local consumers will buy approximately \(D(p)=\frac{4,374}{p^{2}}\) pounds of the coffee per week when the price is \(p\) dollars per pound. It is also estimated that \(t\) weeks from now, the price of Brazilian coffee will be \(p(t)=\) \(0.02 t^{2}+0.1 t+6\) dollars per pound.

1. At what rate will the demand for coffee be changing with respect to price when the price is $9?
2. At what rate will the demand for coffee be changing with respect to time 10 weeks from now? Will the demand be increasing or decreasing at this time?

Price: $2.99

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