Question 1182116
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The minimum value is 2000 at 0 months; the maximum value is 6000 at 6 months.<br>
So the center line is at 4000 and the amplitude is 2000.<br>
The minimum value at 0 months means we can model the population with a negative cosine function with no horizontal shift.<br>
{{{p(t)=-2000*cos(bx)+4000}}}<br>
Half the period (pi radians) is 6 months; so if t is months, then b=pi/6.  So<br>
{{{p(t)=-2000*cos((pi/6)x)+4000}}}<br>
A graph showing a minimum population of 2000 at 0 months and a population of 6000 at 6 months:<br>
{{{graph(400,400,-2,12,-2000,8000,2000,4000,6000,-2000*cos((pi/6)x)+4000)}}}<br>
We want the number of caribou in the population at 1 month:<br>
{{{-2000(cos(pi/6))+4000 = -2000(sqrt(3)/2)+4000 = 4000-1000sqrt(3) = 4000-1732 = 2268}}}<br>