Answer
$c(x(t)) =12e^{2t}-4e^t+5$ and $c(2) =12 e^{4}-4 e^{2}+5$
Work Step by Step
Given $$
c(x)=3 x^{2}-2 x+5 ; x(t)=2 e^{t}
$$
Since $c(x(t))$ given by
\begin{align*}
c(x(t))&=3 x^{2}-2 x+5 \\
&=3 (2 e^{t})^{2}-2(2 e^{t})+5\\
&=12e^{2t}-4e^t+5
\end{align*}
and $c(2) =12 e^{4}-4 e^{2}+5$
