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The number of retro portable CD players you are prepared to supply to a retail outlet every week is given by the formula q = 0.2p^2 + 2p where p is the price it offers you. The retail outlet is currently offering you $70 per CD player. If the price it offers decreases at a rate of $1 per week, how will this affect the number you supply?

Respuesta :

Answer:

Decreasing by 30 per week

Step-by-step explanation:

[tex]q = 0.2p^2 + 2p[/tex]

[tex]\frac{dq}{dt}=0.4p \frac{dp}{dt} + 2\frac{dp}{dt}[/tex]

[tex]\frac{dq}{dt}=(0.4p + 2)\frac{dp}{dt}[/tex]

At p=70,  [tex]\frac{dp}{dt}=-1[/tex]

[tex]\frac{dq}{dt}=(0.4X70 + 2)(-1)[/tex]

[tex]\frac{dq}{dt}=-30[/tex]

The number supplied is decreasing by 30 per week.

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