Question

Suppose the price p, in dollars, and number of sales, x, of an item is related by 5 8 6 50 p x px + + = . If p and x are functions of time, measured in days, find the rate at which x is changing when x = 15, p = 2.90 and dp/dt = -1.15

Answer 1

According to the information of the problem x = 15 , p=2.90 and dp/dt = -1.15

then
`(dx)/(dt) = -3.357\\`

Explanation:

Since everything is changing with respect to time and
`p,x` are related according to the following equation

`5p+5x+3px = 71`

We need to find the implicit derivative with respect to the time. And we get the following.

`5(dp)/(dt)+5(dx)/(dt)+3x(dp)/(dt)+3p(dx)/(dt) = 0`

`(dx)/(dt)` is what we don't know, so we solve for it and get

`(dx)/(dt) = - (5(dp)/(dt)-3x(dp)/(dt))/ (5+3p)`

Now. According to the information of the problem x = 15 , p=2.90 and dp/dt = -1.15

then
`(dx)/(dt) = -3.357\\`