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Thread: Isolate "t" in a cubic function (and sketching equation)

  1. #1
    Junior Member
    Nov 2010

    Isolate "t" in a cubic function (and sketching equation)

    The current through a resistor, in amperes, is I = 4.85 - 0.001t^2
    The resistance, in ohms, is R = 15 +0.11t ( t is in seconds).
    The voltage, in volts, is the product of the current and the resistance.

    How long will it take for voltage to reach 77V, to the nearest second?

    I found V(t) to be V(t) = IR
    Therefore, I just multiplied and brought everything out of the bracket to get:
    v(t) = -0.00011t^3 - 0.015t^2 + 0.5335t + 72.75

    which is what is says in the Answers.

    I subbed V(t) = 77, but now I don't know how to isolate for t. We aren't too familiar with factoring cubic equations, so I'd like some help.
    Thanks. : )

    Also, how would you sketch this function?
    For example, if this was a quadratic equation, I could complete the square to find where the vertex and zeroes are and etc. to sketch it.

    Is there a method similar to completing the square for cubic equations, though?
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  2. #2
    Master Of Puppets
    pickslides's Avatar
    Sep 2008
    Quote Originally Posted by TN17 View Post
    v(t) = -0.00011t^3 - 0.015t^2 + 0.5335t + 72.75
    You can google 'the cubic equation' this will isolate t but I don't recommended it.

    You can graph this by hand using a table of values and the general shape of a cubic.

    If you need to find the zeros of this equation I suggest using technology as it is quite nasty. There is no real equivavlent to completeing the square here that will be nice and clean.
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