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November 23, 2014

November 23, 2014

Posted by **Jo** on Monday, December 7, 2009 at 11:30pm.

I have to find

Foxes are declared to be an endangered species when their population drops below 300. Between what two nonnegative values of "t" were foxes first endangered.

I found one to be about

6.71101496 years i don't know if this is one of the first two how do I deal and how do I find the other one?

- PreCalc -
**Reiny**, Tuesday, December 8, 2009 at 12:45amIn an earlier reply to this same problem to you I had established the equation to be

F = 300sin(5pi/11)(t-4) + 500

I had also shown that this equation satisfies all the data values you gave and it looks like you used it to get your value of 6.7 years.

But remember that the sine is negative in the III and IV quadrants, so I also got a value of t = 7.889 yrs.

Also recall that our period was 4.4, so subtracting 4.4 from any of our answers would produce another set of valid solutions.

6.71 - 4.4 = 2.31

7.889 - 4.4 = 3.49

let's test this

if t = 2.31, F = 300.3

if t = 3.49, F = 300.3

let's take a value between 2.31 and 3.49, how about t=3

F = 203 , which is less than 300

So the foxes were first endangered between the times of 2.3 years and 3.5 years.

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