Precalc

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point) The pressure P (in pounds per square foot), in a pipe varies over time. Four times an hour, the pressure oscillates from a low of 40 to a high of 300 and then back to a low of 40. The pressure at time t = 0 is 40. Let the function P = f(t) denote the pressure in pipe at time t minutes.

Find a possible formula for the function P = f(t) described above.

  • Precalc -

    mean = 340/2 = 170
    amplitude = 300-170 = 130
    min at t = 0 so
    y = 170 - 130 cos(w t) which is 40 at t = 0
    what is w?
    when t = 15 min , w t = 2 pi
    so
    w 15 = 2 pi
    w = (2/15) pi
    so
    y = 170 - 130 cos(2 pi t/15)

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