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Math Help - Two math problems.

  1. #1
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    Two math problems.

    Well, I have been trying to do these two problems for a good while now, and i just feel annoyed to no end.

    I made them in paint to make it easier to see:





    So thanks for any help :]
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  2. #2
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    The second one:

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  3. #3
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    Welcome to the forum.

    For problem 1, surely you can calculate the ratio of the number of elements at time t and the number at time t - 1 for t = 1, ..., 6.

    For problem 2, what do you need to do?
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  4. #4
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    Quote Originally Posted by emakarov View Post
    Welcome to the forum.

    For problem 1, surely you can calculate the ratio of the number of elements at time t and the number at time t - 1 for t = 1, ..., 6.

    For problem 2, what do you need to do?
    Thanks :]

    Uhm for problem two you basically have to graph the line I guess. From what I know it's supposed to be a curvy line that goes through three points on this graph. I just don't know where the points belong and whatever it goes into a negative or postive curve.
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  5. #5
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    You can easily find roots of f(x), i.e., x such that f(x) = 0. A product is zero iff at least one of the factors is 0. You can also determine whether f(x) is positive or negative between the roots by substituting some value between those roots for x. For example, when 0 < x < 6, we can take x = 1. Then we have: -x < 0, x + 2 > 0, (x + 9)^2 > 0, x - 6 < 0, i.e., there are two negative and two positive factors. All in all, f(x) > 0 when 0 < x < 6.

    Note that f(x) has the same sign to the left and to the right of -9 because x + 9 occurs squared. For other roots, f(x) have opposite signs immediately to the left and to the right of those roots.
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