Question

If Margret runs a business, and this year's revenue is given by the function r=0.5x2−200x, what does the coefficient of x2 represent in the context of the revenue function?

A) The constant term in the revenue
B) The linear term in the revenue
C) The quadratic term in the revenue
D) The rate of change of revenue

Answer 1

The coefficient of x² in the revenue function r=0.5x²−200x represents the rate of change of revenue as more goods are sold, signaling a quadratic relationship in revenue growth.

Step-by-step explanation:

In the context of the revenue function r=0.5x²−200x provided by the student, the coefficient of x², which is 0.5, represents the rate of change of revenue with respect to the quantity of goods sold as the number increases. This is because the term x² signifies a quadratic relationship in the equation, which means that the revenue does not grow at a constant rate, but accelerates as the quantity increases. The coefficient tells us how much the revenue will increase for each additional unit squared, which can affect the overall shape of the revenue curve and indicate important economic factors such as economies of scale.