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Thread: another problem with quadratic equation

  1. #1
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    another problem with quadratic equation

    The number of of employees n(a) of a company that has existed for 15 years has increased during the first 5 years but has been decreasing since. This problem can be written as n(a) = -8(a-5)^2 + 230 in which a represents the number of years since the company started. During how many years the number of employees was higher than the number of employees when the company started?
    Is the initial number of employees 230? If it is here's what I tried: 231 = -8(a-5)^2 + 230 I substract 230 from both sides. so... 1 = -8(a-5)^2 After this I don't know what to do. And if that equation isn't right then I'm even more confused!
    thanks
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  2. #2
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    Re: another problem with quadratic equation

    OK. You are absolutely correct that the company had 230 employees to start with.

    $a = 231 \implies n(a) > 230.$ That is perfectly correct but useless.

    What the question is in mathematical terms is $ n(a) > 230 \implies what\ values\ of\ a.$

    Your way would require looking at 232, 233, 234, etc in addition to 231. Technically you need in inequation, not an equation. You need

    $-\ 8(a - 5)^2 + 230 > 230 \implies -\ 8(a - 5)^2 > 0.$

    Make sense?

    Now to solve an inequation you first solve the related equation. So step 1 is to solve

    $-\ 8(a- 5)^2 = 0.$

    Can you do that? If so, what next?
    Last edited by JeffM; Feb 3rd 2017 at 07:38 AM.
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  3. #3
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    Re: another problem with quadratic equation

    No, you are not correct that the number of employees when the company started was 230! You are told that "a represents the number of years since the company started." So the company started when a= 0. That gives n(0)= -8(0- 5)^2+ 230= -200+ 230= 30. The companies number of employees increased in the first 5 years so a(5)= 230 was the maximum number of employees the company had.

    You want to solve the inequality -8(a- 5)^2+ 230> 30. That is equivalent to (a- 5)^2< 25.
    Thanks from JeffM
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  4. #4
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    Re: another problem with quadratic equation

    Oh my. Some days I am an idiot. If my post can be deleted that would be great.
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