Government economists of a developing country determined that the purchase of im

Question

Government economists of a developing country determined that the purchase of imported perfume is related to a proposed "luxury tax" by the following formula where N(x) measures the percentage of normal consumption of perfume when a "luxury tax" of x% is imposed on it. N(x) = squareroot 10, 000 - 40x - 0.02x^2 (0 lessthanorequalto x lessthanorequalto 200) Find the rate of change of N(x) for taxes of 15%, 100%, and 125%. (Round your answers to three decimal places.) 15% tax consumption/percentage increase in tax 100% tax consumption/percentage increase in tax 125% tax consumption/percentage increase in tax

Explanation / Answer

N'(x) = 1/2(10,000-40x-0.02x2)-1/2 (-40-0.04x)

Now for x=15

N'(15) = 1/2(10,000-600-4.5)-1/2(-40-.6) = (1/2)(9395.5)-1/2(-40.6)=-0.209

For x = 100

N'(100) = 1/2(10,000-4000-200)-1/2(-40-4) = -0.289

For x = 125

N'(125) = 1/2(10000-5000-312.5)-1/2(-40-5) = -0.329

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