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15)The demand equation for a certain product is given by the formulap = 32-10.0001x+1where x is the number of units sold in a month and p is the price perunit. If the price is set at $14.75 for the month, how many units will be sold?

15)The demand equation for a certain product is given by the formulap = 32-10.0001x-example-1
User Derferman
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The demand equation is given to be:


p=32-√(0.0001x+1)

where p is the price and x is the number of units sold.

If the price per unit is $14.75, the number of units will be calculated as follows:


\begin{gathered} p=14.75 \\ \therefore \\ 14.75=32-√(0.0001x+1) \end{gathered}

Subtracting 32 from both sides, we have:


\begin{gathered} -√(0.0001x+1)=14.75-32 \\ -√(0.0001x+1)=-17.25 \end{gathered}

Multiply both sides by -1:


√(0.0001x+1)=17.25

Square both sides:


\begin{gathered} 0.0001x+1=17.25^2 \\ 0.0001x+1=297.5625 \end{gathered}

Subtract 1 from both sides:


\begin{gathered} 0.0001x=297.5625-1 \\ 0.0001x=296.5626 \end{gathered}

Divide both sides by 0.0001:


\begin{gathered} x=(296.5625)/(0.0001) \\ x=2965625 \end{gathered}

The number of units sold will be 2,965,625 units.

User Kay Wu
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