Question

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?

Answer 1

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.