Question

The annual demand q for bottles of wine from a vineyard when the bottles are priced at p dollars each satisfies the equation
qe0.04p = 6000.
The price is currently $12 per bottle. Find the rate at which demand changes (with respect to time) if the price increases at a rate of $1.20 per year. (Round your answer to the nearest whole number.)

Answer 1

-178 bottles per year

Answer 2

q e^(.04 p) = 6000
so
q = 6000 e^(-.04 p)
dq/dt = 6000 (-.04)e^(-.04 p) dp/dt
p = 12 and dp/dt = 1.2
dp/dt = -240 [e^(-0.48)] (1.2)
= -240 * .619 * 1.2 = - 178
agree