Problem Solving

BTGmoderatorDC wrote:


A certain manufacturer uses the function \(C(x) = 0.04x^2 - 8.5x + 25,000\) to calculate the cost, in dollars, of producing x thousand units of its product. The table above gives values of this cost function for values of x between 0 and 50 in increments of 10. For which of the following intervals is the average rate of decrease in cost less than the average rate of decrease in cost for each of the other intervals?

A. From x = 0 to x = 10
B. From x = 10 to x = 20
C. From x = 20 to x = 30
D. From x = 30 to x = 40
E. From x = 40 to x = 50

OA E

Source: Official Guide

Brute force approach is the best approach for these kinds of questions. From From x = 0 to x = 10, the average rate of decrease in cost = 25,000 - 24,919 = 81; while From From x = 40 to x = 50, the average rate of decrease in cost = 24,724 - 24,675 = 49. Usually, for these kinds of questions, the average rate of decrease in cost would either decrease or increase. In this case, it is decreasing; thus, the correct answer is From x = 40 to x = 50.

The correct answer: E

Hope this helps!

-Jay
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BTGmoderatorDC wrote:


A certain manufacturer uses the function \(C(x) = 0.04x^2 - 8.5x + 25,000\) to calculate the cost, in dollars, of producing x thousand units of its product. The table above gives values of this cost function for values of x between 0 and 50 in increments of 10. For which of the following intervals is the average rate of decrease in cost less than the average rate of decrease in cost for each of the other intervals?

A. From x = 0 to x = 10
B. From x = 10 to x = 20
C. From x = 20 to x = 30
D. From x = 30 to x = 40
E. From x = 40 to x = 50


OA E

Source: Official Guide

Since each interval has the same length (10 units), the interval that has the lowest average rate of decrease in cost is the interval that has the smallest decrease. Therefore, we can just calculate the decrease in each interval.

A. From x = 0 to x = 10: the decrease is 25,000 - 24,919 = 81.

B. From x = 10 to x = 20: the decrease is 24,919 - 24,846 = 73.

C. From x = 20 to x = 30: the decrease is 24,846 - 24,781 = 65.

D. From x = 30 to x = 40: the decrease is 24,781 - 24,724 = 57.

E. From x = 40 to x = 50: the decrease is 24,724 - 24,675 = 49.

Answer: E