Answer
$V_C = 1000~e^{-t}$
Work Step by Step
We can find an expression for $V_C$:
$V_C = \frac{q}{C}$
$V_C = \frac{q_0~e^{-t/RC}}{C}$
$V_C = \frac{(1.0\times 10^{-3}~C)~e^{-t/(1.0\times 10^6~\Omega)(1.0\times 10^{-6}~F)}}{1.0\times 10^{-6}~F}$
$V_C = \frac{(1.0\times 10^{-3}~C)~e^{-t/1}}{1.0\times 10^{-6}~F}$
$V_C = 1000~e^{-t}$
