Calculus

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.)

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  1. -178 bottles per year

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  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

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    Damon

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