the productivity of a person at work (on a scale of 0-10) is modeled by a cosine function: 5cos (pie/2t) +5, where t is in hours. If the person starts work at t=0, being 8:00 am, at what times is the worker the least productive?
a) 12pm
B) 10 am and 2pm
C) 11 am and 3 pm
D) 10 am,12pm and 2 pm
To find the times when the worker is the least productive, we need to identify the minimum points on the cosine function. In general, the cosine function oscillates between -1 and 1, so to find the minimum points, we need to find the values of t that make the expression 5cos(pi/2t) + 5 equal to the smallest possible value.
Since the cosine function has a period of 2π (or 360 degrees), and the coefficient of t is π/2 in our function, we can conclude that the period of the given function is 4. This means that the function repeats every 4 units of time.
Given that the worker starts work at t = 0 (8:00 am), we can determine that the first repetition of the function occurs at t = 4 (12:00 pm). At this time, the cosine function is at one of its maximum points, and hence the worker is the most productive.
Since the period of the function is 4, the function will reach its minimum point halfway through the period. Therefore, the halfway point between 0 and 4 is t = 2 (10:00 am). At this time, the worker is the least productive.
So the answer is B) 10 am and 2 pm.