An importer of Brazilian coffee estimates that local consumers will buy approxim

Question

An importer of Brazilian coffee estimates that local consumers will buy approximately D(p)=4414/p2 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)=0.01t^2+0.05t+6 dollars per pound

a) At what rate will the demand for coffee be changing with respect to price when the price is 8 dollars?

b) At what rate will the demand for coffee be changing with respect to time 10 weeks from now?

c) Is the demand increasing after 10 weeks? Answer (Y/N):

Explanation / Answer

a) D = 4414/p^2

dD/dp = 4414*(d/dp of p^-2)

dD/dp = 4414 * -2/p^3

-8828/p^3

Plug in p = 8 :

-8828 / 8^3

-17.2421875 --> FIRST ANSWER

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dD/dt = -8828/p^3 * (dp/dt)

p(t)=0.01t^2+0.05t+6

p(10) = 0.01(10^2) + 0.05(10) + 6
p(10) = 7.5

dp/dt = 0.02t + 0.05
dp/dt at t = 10 ---> 0.02(10) + 0.05 --> 0.25

= -8828/(7.5)^3 * 0.25

= -5.2314 ---> SECOND ANSWER

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c) Since dD/dt is NEGATIVE, the demand is actually DECREASING

So, NO

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