HW2 4 to 2 5: Problem 16 Previous Problem ListNext t point) An importer of Brazl

Question

HW2 4 to 2 5: Problem 16 Previous Problem ListNext t point) An importer of Brazlian coffestimates that local consumers will by approximately D(p) pounds of the coffee per week when the price is pdollars per pound. It is also estimated that t weeks from now, the price of Brazilian coffee will be 1304 p(t)-0.02? + 0.1t + 6 dollars per pound a) At what rate wll the demand for coffee be changing with respect to price when the price is 9 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 ater 10 weeks? Answer (Y/N) Note: You can ean partial credit on this probiem

Explanation / Answer

D(p) = 4304 p^(-2)

D'(p) = 4304* (-2) p^(-3) = -8608/p^3

set p=9

D'(p) = -8608/9^3 = 11.8079= -$11.8079 per pound (decrease)

b)

p(t)=0.02t^2+0.1t+6

p'(t) = 0.04t +0.1

when t=10

p(t)=9

p'(t) = 0.04(10)+0.1 = .4+.1 = 0.5 pounds

Rate of change of demand=

D'(t)=(-8608/p^3)p'(t=10)

D'(t)=(-8608/9^3)*0.5=-5.904 pounds/week

C) no the demand isn't increasing,it's decreasing!

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