The rate of change in sales volume when the price is $22 is -0.107 and When the price increases $1, the sales volume will decrease by -48
The rate of change formula gives the relationship describing how one quantity changes in relation to the change in another quantity
According to the question,
y denotes the weekly sales volume and p denotes the price per unit
Equation is [tex]y = \frac{32}{3p + 1^{\frac{-2}{5}}}[/tex]
(a) We have to find the rate of change in sales volume when price is $22
Differentiating the equation w.r.t p,
[tex]\frac{dy}{dp} = \frac{-32(3)}{(3p + 1^\frac{-2}{5})^2}[/tex]
Putting value of p = 22
=> [tex]\frac{dy}{dp} = \frac{-32(3)}{(3(22) + 1^\frac{-2}{5})^2}[/tex]
=> -96 / (66 + 1 - 2(22)(1))²
=> -96 / 897
=> -0.107
(b) To find If the price increases $1, the sales volume will decrease by
Replacing p = 1
=> dy/dp = -96/2
=> -48
To know more about Rate of change here
https://brainly.com/question/29518179
#SPJ4
