A quadratic trend equation y_t = 900 + 30t - 2.5t² was fitted to a company's sales. This result implies that the sales trend: A)hit a maximum in period t = 30. B)hit a maximum in period t = 6. C)hit a minimum in period t = 5. D)hit a minimum in period t = 6.

Question

Quizplus · Accepted Answer

DThe quadratic trend equation given is of the form $y = 900 + 30t - 2.5t^2$. The coefficient of $t^2$ is negative (-2.5), indicating that the parabola opens downwards, which means the vertex of the parabola represents a maximum point. The time $t$ at which this maximum occurs can be found using the vertex formula $t = -\frac{b}{2a}$, where $a = -2.5$ and $b = 30$. Substituting these values gives $t = -\frac{30}{2(-2.5)} = 6$, indicating that the sales trend hits a maximum in period $t = 6$, not a minimum. Therefore, choices B (maximum at $t = 6$) and D (minimum at $t = 6$) are correct in the context of identifying the period at which a significant point occurs, but the correct interpretation is that it hits a maximum at $t = 6$, making B the accurate choice in terms of the trend's behavior. Choice D is incorrect upon reevaluation because the trend hits a maximum, not a minimum, at $t = 6$.

A Quadratic Trend Equation Yt = 900 + 30t -

A Quadratic Trend Equation Y_t = 900 + 30t -