Question

Sharon was going through the financial records of her company. The profit earned by the company, p(t), over time t, in years, for five consecutive years can be modeled by a quartic function. Each of the following functions is a different form of the quartic model for the situation given above. Which form would be most helpful if attempting to determine the time at the which the company did not earn any profit?
a.p(t) = 40(t - 3)(t + 2)(t - 5)(t + 3)


b.p(t) = 40(t2 - t - 6)(t2 - 2t - 15)


c.p(t) = 40t(t3 - 3t2 - 19t + 27) + 3,600


d.p(t) = 40t4 - 120t3 - 760t2 + 1,080t + 3,600

Answer 1

For this case what we must do is find a quadratic function that is already factored.
 This is because in the factored quadratic equations, it is easier to observe the zeros of the function.
 In this case, the zeros of the function represent the time at which the company did not make any profit.
 We have the following equation:
 p (t) = 40 (t - 3) (t + 2) (t - 5) (t + 3)
 We observed that there was no gain in:
 t = 3
 t = 5
 The other roots are discarded because they are negative
 Answer:
 a.p (t) = 40 (t - 3) (t + 2) (t - 5) (t + 3)