Question 1040811: What does each number represent in this equation?
R = 1200 + 250 sin 1/2πt
Image of reference: https://i.imgsafe.org/584044b530.png
I understand R is the number of rabbits ( 1200 ) I think 250 is the number of coyotes.
What does sin 1/2πt represent?
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! 1200 is the middle-most or average value of the population. It's right in the middle of the max and min.
the 250 represents the amplitude. This is the distance from the middle (1200) to either the peak or valley. It determines how tall the sine curve is. A larger magnitude means the population fluctuates more.
the "sin" refers to "sine" which is a trigonometric function. All sine curves go up and down forever like an ocean wave. Many things in nature are periodic (eg: population counts, tidal heights, etc) so sine curves are used a lot.
the (1/2)pi*t part is useful in determining the period. This is the time it takes to complete one full cycle. In this case, it's 2pi/B = 2pi/(0.5pi) = 4 years. It takes 4 years for the population to go through a full cycle.
Side note: while populations do go through cycles, a logistic curve may be more appropriate to use as a model.
Another side note: While a coyote is shown on the graph and mentioned in the problem, none of the numbers refer to the coyote population. Rabbits have other predators and other things that could kill them (eg: bad weather or habitat destruction from humans). There are also other factors that help them flourish (eg: good weather, habitat conservation). The coyote part was probably put in there to throw you off.
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