Let $C(x)$ be the total cost in dollars of electricity used by a factory from time $t=0$ to $t=x$ hours, where the cost rate is given by $c\left(t\right)=\begin{cases}0.5t+3;t\le4\\ 5;t>4\end{cases}$.
Find the formula for $C(x)$.

$C\left(x\right)=\begin{cases}0.5x^2+3;0\le x\le4\\ 5;x>4\end{cases}$

$C\left(x\right)=\begin{cases}0.25x^2+3x;0\le x\le4\\ 5x-4;x>4\end{cases}$

$C\left(x\right)=\begin{cases}0.25x^2+3;0\le x\le4\\ 5;x>4\end{cases}$

$C\left(x\right)=\begin{cases}0.5x^2+3;0\le x\le4\\ 5x-4;x>4\end{cases}$