Question

The demand function for q units of a product at $p per unit is given by p(q+1)2=300,000. Find the rate of change of quantity with respect to price when p=$120. Interpret this result. If the price is increased by $1.00, the demand will by units.

Answer 1

The rate of change of quantity with respect to price when p=$120 is 26,208 units per price change. For every $1 increase in price, the quantity demanded will increase by 26,208 units.

Step-by-step explanation:

To find the rate of change of quantity with respect to price, we need to differentiate the demand function with respect to price. Differentiating the given demand function p(q+1)^2=300,000 with respect to p gives us 2(q+1)^2. Plugging in the value p=$120 into the derivative, we get 2(120+1)^2 = 26,208. Therefore, the rate of change of quantity with respect to price when p=$120 is 26,208 units per price change.

Interpreting this result, it means that for every $1 increase in price, the quantity demanded will increase by 26,208 units.