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 % is imposed on it. N(x) = 10,000 - 40x -0.02x2 (0 SX s 200) Find the rate of change of M(x) for taxes of 40%, 100%, and 140%. (Round your answers to three decimal places.) 40% tax consumption/percentage increase in tax 100% tax consumption/percentage increase in tax 140% tax consumption/percentage increase in tax Need Help? Read It -/1 points TANAPMATH7 9.6.083. My Notes Ask Your Teacher The quantity demanded per month, x, of the Zephyr tablet computer is related to the average unit price, p in dollars), of tablet computers by the equation x= f(p) = 100 810,000 - p2 It is estimated that t months from now, the average price of a tablet computer will be given by PC) = 1 + 1 + 200 (Osts 60) dollars. Find the rate at which the quantity demanded per month of the tablet computers will be changing 25 months from now. (Round your answer to one decimal place.) computers/month

Answer 1

The objective is to find the rote of change of n(x) for taxes of 10%, 100%," and 1454 N(x) = 10,000 - 402-0.02x² (0<x<200) Differentiate with respect to xas follows N'(d) --40-20.02% (03x3200) for 10% Rate of change is given by Rate = -40-2x0.02x610) = -40 -0.4 = -40.4 For 100%. Rate of change is given by Rate = – 40 - 2x0.02 (100) - 404 = -44 For 1451. Rate of change is given by Rate of chra = -40 - 2 x 0.02 (145) -- – 40 - 5.8 = -45.8