Brief Calculus.

Question

The demand function for a product is given by p(n) = 460 - 0.65n², where p is the price in dollars and n is the quantity in thousands. If adverse weather conditions are driving the price up by $9 per week, find the rate at which the demand quantity for the product is changing when the price is $200. The demand for this product is falling or rising by ............... thousand items per week. ( give at least four decimal places)

Answer 1

p(n)=460-0.65n²

dp/dt = -1.3n dn/dt

dn/dt = (dp/dt)/(-1.3n)

When dp/dt = $9 per week and p = $200

200=460-0.65n² --> n = 20

dn/dt = 9/(-1.3•20) = -0.3462 thousand items per week or falling by 0.3462 thousand items per week