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The Political Noise Problem. The amount of background noise is important to television news reporters. One station developed the formula showing the noise level in decibels (N) as it relates to the time after the speaker stops talking in seconds (t). Use the equation below to compute how many seconds after the speaker stops will the noise level be the greatest? Write and tell how you decided

N = t^2 + 12t + 54

  • Math -

    Something is not right about your equation.
    The way it is, it would be a parabola opening upwards, and of course it would not have a maximum, but rather a minimum value of N
    Are you sure the first term wasn't -t^2 ?

  • Math -

    I assume you don't know calculus, so you will have to use the "completing the square" technique (or graphing) to find the t value for which N is greatest.

    N = t^2 + 12t + 54
    = t^2 + 12t + 36 + 18
    = (t+6)^2 + 18

    That is SMALLEST when t = -6. I assume you are only interested in t>0. There is no maximum. Are you sure you didn't mean to write
    N = t^2 - 12t + 54 ?

  • Math -

    Sorry, Yes the correct equation is

    -t^2 + 12t + 54

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