Expert: Ahmed Salami - 10/8/2004

Question
in a certain electric circuit, the available power P (in watts), depends on the current, I (in amperes), that is flowing, as shown in this chart.

I    1    2    3
P   99  176  231

a) find the quadratic function, P(I), that models the relationship between the power and the current.
b) find the maximum possible power.

Answer
Hi Amy,
I'm really sorry about the delay. We had a technical problem around here.
Using the method of least squares for the curve fitting, the function is
P = 110(I) - 11(I)^2
The maximum power occurs when dP/dI = 0. But
dP/dI = 110 - 22(I)
equating to zero gives
I = 5
and consequently, P(max)= 275
I hope that you're okay with this.
Regards.