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

1. ## 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?

2. Originally Posted by TN17
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.