If a fitted trend equation is y_t = 120 - 40t + 2.5t², then the turning point will be: A)a peak in period 40. B)a trough in period 5. C)a peak in period 4. D)a trough in period 8.

Question

Quizplus · Accepted Answer

To find the turning point, we need to find the maximum or minimum point of the curve. This will occur when the first derivative of the equation is equal to zero, and the second derivative is negative (for a maximum) or positive (for a minimum). Taking the first derivative of the equation, we get:

y' = -40 + 2.5t

Setting y' = 0, we get:

2.5t = 40

t = 16

So the turning point occurs at t = 16. To determine whether this is a maximum or minimum, we take the second derivative:

y'' = 2.5

Since y'' is positive, the turning point at t = 16 is a minimum. Therefore, the answer is D, a trough in period 8.

If a Fitted Trend Equation Is Yt = 120 -

If a Fitted Trend Equation Is Y_t = 120 -