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.
