A quadratic trend equation was estimated from monthly sales of trucks in the United States from July 2006 to July 2011. The estimated trend is y_t = 106 + 1.03t + 0.048t², where y_t units are in thousands. From this trend, how many trucks would be sold in July 2012? A)About 308,419 B)About 524,889 C)About 436,982 D)About 223,831

Question

Quizplus · Accepted Answer

To find the number of trucks sold in July 2012, we need to substitute t = 72 (since July 2006 is t = 1, July 2007 is t = 13, and so on) into the trend equation:

y = 106 + 1.03t + 0.048t^2

y = 106 + 1.03(72) + 0.048(72)^2

y = 106 + 74.16 + 208.13

y = 388.29

However, the units of the trend equation are in thousands, so we need to multiply by 1000:

y = 388.29 * 1000

y ≈ 436,982

Therefore, the best choice is C, which is about 436,982.

A Quadratic Trend Equation Was Estimated from Monthly Sales of Trucks