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Demand for your tie-dyed T-shirts is given by the formula q = 510 − 90p0.5 where q is the number of T-shirts you can sell each month at a price of p dollars. If you currently sell T-shirts for $15 each and you raise your price by $2 per month, how fast will the demand drop? (Round your answer to the nearest whole number.)

Respuesta :

Answer:

The demand will drop approximately 23 T-shirt per month.

Step-by-step explanation:

Consider the provided formula.

[tex]q = 510-90p^{0.5}[/tex]

You currently sell T-shirts for $15 each and you raise your price by $2 per month,

That means p=$15 and [tex]\frac{dp}{dt}=2[/tex]

We need to find how fast demand will drop.

So differentiate the above function with respect to time.

[tex]\frac{dq}{dt} =0-45p^{0.5-1}\frac{dp}{dt}[/tex]

[tex]\frac{dq}{dt} =-45p^{-0.5}\frac{dp}{dt}[/tex]

Substitute the respective values as shown:

[tex]\frac{dq}{dt} =-45(15)^{-0.5}(2)[/tex]

[tex]\frac{dq}{dt} \approx-23.24[/tex]

Hence, the demand will drop approximately 23 T-shirt per month.