SOLUTION: The population of a caribou herd varies sinusoidally with a period of one year. The population is at a minimum at the beginning of the year when the population is about 2000 animal

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Question 1182116: The population of a caribou herd varies sinusoidally with a period of one year. The population is at a minimum at the beginning of the year when the population is about 2000 animals. The population is at a maximum of 6000 animals after 6 months. How many caribou are there expected to be at the end of 1 months? Round to the nearest whole number.
Answer by greenestamps(13195) About Me  (Show Source):
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The minimum value is 2000 at 0 months; the maximum value is 6000 at 6 months.

So the center line is at 4000 and the amplitude is 2000.

The minimum value at 0 months means we can model the population with a negative cosine function with no horizontal shift.

p%28t%29=-2000%2Acos%28bx%29%2B4000

Half the period (pi radians) is 6 months; so if t is months, then b=pi/6. So

p%28t%29=-2000%2Acos%28%28pi%2F6%29x%29%2B4000

A graph showing a minimum population of 2000 at 0 months and a population of 6000 at 6 months:



We want the number of caribou in the population at 1 month: