Sinosoid graph problem

1. Feb 20, 2008

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, occured when t = 2.9 years. The next maximum, 800 foxes, occured 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.

2. Feb 21, 2008

Ouabache

Welcome to PF forums!! You will find a lot of useful information here and plenty of knowledgable 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 thread 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.

3. Feb 21, 2008

HallsofIvy

Staff Emeritus
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?