Question

The number of bottles of whiskey that a store will sell in a month at a price of p dollars per bottle is . N(p) = (2250)/(p+3) Find the rate of change of this quantity when the price is $7.

Answer 1

Answer: The rate of change of this quantity would be -22.50.

Step-by-step explanation:

Since we have given that

the number of bottles of whiskey that  a store will sell in a month at a price of p is given by

$N(p)=\dfrac{2250}{p+3}$

We need to find the rate of change of this quantity:

So, we will find the first derivative with respect to p.

$N'(p)=2250(-1)(p+3)^{-2}$

if p = 7 , then the rate of change becomes,

$N'(7)=-2250(7+3)^{-2}=\dfrac{-2250}{10^2}=\dfrac{-2250}{100}=-22.50$

Hence, the rate of change of this quantity would be -22.50.