Question

Michael works in the marketing department of a company. He recorded the sales of his company for 10 consecutive months. The amount of sales, n(t), over time t, in months, can be modeled by a cubic function.

Each of the following functions is a different form of the cubic model for the situation given above. Which form would be the most helpful if attempting to determine the number of months after which the sales were approximately constant?

A) n(t) = 0.1(t - 8)3 + 51.2

B) n(t) = 0.1t2(t - 24) + 19.2t

C) n(t) = 0.1t3 - 2.4t2 + 19.2t

D) n(t) = 0.1(t3 - 24t2 + 192t)

Answer 1

A) n(t) = 0.1(t - 8)3 + 51.2

Answer 2

The correct answer would be option:A

Explanation:

since in all the option we are given a cubic function also all the functions are equal. (by expanding the terms in each of the options we can check that all are equal)

But through the representation in option A) we could easily find out the inflection point as well as critical point of the function. It is the easiest way of expressing a cubic polynomial so that the derivative of a function could be easily calculated.

Hence, the correct option is A.