The function gives the rate of change of profit for a new business during its first year. The input is the number of months since the business opened, and the output units are millions of dollars per month. What is the interpretation, in context, of the accumulation function ?
A) is how fast the profit, in millions of dollars, is changing at x months.
B) is the number of months it will take to make x millions of dollars.
C) is the amount of profit, in millions of dollars, the business made in month x.
D) is the amount of profit, in millions of dollars, the business made after month x in its first year.
E) is the amount of profit, in millions of dollars, the business has made in its first x months.

Question

The function  gives the rate of change of profit for a new business during its first year. The input is the number of months since the business opened, and the output units are millions of dollars per month. What is the interpretation, in context, of the accumulation function  ?
A) is how fast the profit, in millions of dollars, is changing at x months. 
B) is the number of months it will take to make x millions of dollars. 
C) is the amount of profit, in millions of dollars, the business made in month x. 
D) is the amount of profit, in millions of dollars, the business made after month x in its first year. 
E) is the amount of profit, in millions of dollars, the business has made in its first x months.

Quizplus · Accepted Answer

The accumulation function is typically the integral of the rate of change function. In this case, the accumulation function would give the total profit made by the business up to a certain number of months since opening. Therefore, choice E is the best interpretation since it describes the total profit the business has made in its first x months.

The Function Gives the Rate of Change of Profit