A price (in dollars) and demand for a product are related by
If the price is increasing at a rate of 2 dollars per month when the price is 20 dollars, find the rate of change of the demand.
Rate of change of demand =
To find the rate of change of the demand, we need to find the derivative of the demand function with respect to the price. Since the price and demand are related, we can assume that there is a demand function D(P), where P represents the price.
Given that the price is increasing at a rate of 2 dollars per month and the price is currently 20 dollars, we can express the price as a function of time, P(t) = 20 + 2t, where t represents time in months.
Now we can differentiate the demand function with respect to time:
dD/dt = dD/dP * dP/dt
Since we are looking for the rate of change of the demand with respect to time, we can rearrange the equation to solve for dD/dt:
dD/dt = (dD/dP) * (dP/dt)
To find the first derivative, dD/dP, we need to know the specific function relating price and demand. Since that information is not given in the question, we cannot determine the rate of change of the demand without further information.