Fox Population Sinusoidal Graph and Equation | Endangered Species Prediction

[Aphrodite08]

Here is the problem:

Naturalists find that the poplulations of some kinds of predatory animals vary periodically. Assume that the population of foxes in a certain forest varies sinusoidally with time. Records started being kept when time t = 0. A minimum number, 200 foxes, occurred when t = 2.9 years. The next maximum, 800 foxes, occurred at t = 5.1 years.

a.) Sketch a graph of this sinuoid.
b.) Write an equation expressing the number of foxes as a function of time,
t.
c.) Predict the population when t = 7
d.) Foxes are declared to be an endangered species when their population drops below 300. Between what two non-negative values of t were foxes first endangered?

I do not know how this graph should look like... as in whether it should be sine or cosine, and how I would properly show the minimums and maximums. Any help would be appreciated.

 

[Ouabache]

Welcome to PF forums! You will find a lot of useful information here and plenty of knowledgeable people who can assist you.

You need to offer your attempt at a solution. Just show us what you think so far. Don't worry if it is wrong, we can help you. Also please be sure to reread this https://www.physicsforums.com/showthread.php?t=94381 which appears at the top of this topic..

Let me mention that you're off to a good start. You've stated your problem. If after thinking about this, you still are not making any progress. Why not start by telling us the general equation for a sinusoidal function being sure to define how the variables correspond to the graphical representation.

 

[HallsofIvy]

Here is the problem:

Naturalists find that the poplulations of some kinds of predatory animals vary periodically. Assume that the population of foxes in a certain forest varies sinusoidally with time. Records started being kept when time t = 0. A minimum number, 200 foxes, occurred when t = 2.9 years. The next maximum, 800 foxes, occurred at t = 5.1 years.

a.) Sketch a graph of this sinuoid.
b.) Write an equation expressing the number of foxes as a function of time,
t.
c.) Predict the population when t = 7
d.) Foxes are declared to be an endangered species when their population drops below 300. Between what two non-negative values of t were foxes first endangered?

I do not know how this graph should look like... as in whether it should be sine or cosine, and how I would properly show the minimums and maximums. Any help would be appreciated.

It really doesn't matter whether the curve is a "sine" or "cosine"- they look the same. The difference is where you choose to set t= 0. Since you are told that "record keeping" started ast t= 0, you are given that and I suspect the result is neither a pure "sin(t)" nor "cos(t)". Try, instead $Asin(\omega(t- t_0))$ or [itex]A cos(\omega(t- t_0)). Where will either of those have a maximum, where a mininum?