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Math Help - marginal revenue

  1. #1
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    marginal revenue

    marginal revenue function:
    dr/dq=(50-4q)e^(-r/5)

    find the demand equation

    i dont even know where to start for this one, but its related to differential equations

    any help is appreciated!
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by s0urgrapes View Post
    marginal revenue function:
    dr/dq=(50-4q)e^(-r/5)

    find the demand equation

    i dont even know where to start for this one, but its related to differential equations

    any help is appreciated!
    This is a seperable differential equation.

    \frac{dr}{dq}=(50-4q)e^{-r/5} moving around some stuff we get..

    e^{r/5}dr=(50-4q)dq so now we integrate both sides.

    \int e^{r/5}dr=\int (50-4q)dq \iff 5e^{r/5}=-2q^2+50q+C

    If we want we can solve the equation for r

    e^{r/5}=-\frac{2}{5}q^2+10q+\frac{C}{5} taking the ln of both sides.

    \frac{r}{5}=ln \left[-\frac{2}{5}q^2+10q+\frac{C}{5} \right]

    r=5ln \left[-\frac{2}{5}q^2+10q+\frac{C}{5} \right]
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