Suppose that the numbers W (in thousands) of construction workers employed in the United States during 2006 can be modeled by $W = 9094 + 455.2 \sin ( 0.6 t - 1.813 )$ where t is the time in months, with $t = 1$ corresponding to January 1. Approximate the month t in which the number of construction workers employed was a maximum. What was the maximum number of construction workers employed? Round your answer to nearest hundredth.
A)July; The maximum number of construction workers employed is 9559.
B)May; The maximum number of construction workers employed is 9539.
C)June; The maximum number of construction workers employed is 9539.
D)May; The maximum number of construction workers employed is 9549.
E)June; The maximum number of construction workers employed is 9549.

Question

Quizplus · Accepted Answer

The maximum value of the sine function is 1, so to find the maximum number of construction workers, we substitute 1 into the equation: $W_{max} = 9094 + 455.2 \times 1 = 9549.2$, rounding to 9549. To find the month, we set the sine function's argument equal to $\pi/2$ (where sine is 1), so $0.6t - 1.813 = \pi/2$. Solving for $t$ gives a value in the range of June, hence option E is correct.

Suppose That the Numbers W (In Thousands) of Construction Workers W=9094+455.2sin⁡(0.6t−1.813)W = 9094 + 455.2 \sin ( 0.6 t - 1.813 )W=9094+455.2sin(0.6t−1.813)

Suppose That the Numbers W (In Thousands) of Construction Workers $W = 9094 + 455.2 \sin ( 0.6 t - 1.813 )$