Answer
$P = 4.50\times 10^{-4}~W$
Work Step by Step
We can find the voltage at $t = 0.500~s$:
$V = 6.00+(4.00)(0.500)-(2.00)(0.500)^2$
$V = 7.50~V$
We can find the current at $t = 0.500~s$:
$Q = C~V$
$i = \frac{dQ}{dt} = C~\frac{dV}{dt}$
$i = C~(4.00-4.00~t)$
$i = (30~\mu F)~[4.00-4.00~(0.500)]$
$i = (30~\mu F)~(2.00~V/s)$
$i = 60.0~\mu A$
We can find the power output:
$P = i~V$
$P = (60.0~\times 10^{-6}~A)(7.50~V)$
$P = 4.50\times 10^{-4}~W$
