Answer
$$0.3567\ \text{kg}/\text{year}$$
Work Step by Step
Given $$W(t)=\left(3.46293-3.32173 e^{-0.03456 t}\right)^{3.4026}$$
Since
\begin{align*}
W'(t)& =3.4026\left(3.46293-3.32173 e^{-0.03456 t}\right)^{2.4026} \left(0.1147989 e^{-0.03456 t}\right) \\
&=0.3906147 e^{-0.03456 t}\left(3.46293-3.32173 e^{-0.03456 t}\right)^{2.4026}
\end{align*}
Then the rate of change at $t=10$ is
\begin{align*}
W'(10) &=0.3906147 e^{-0.03456(10)}\left(3.46293-3.32173 e^{-0.03456 (10)}\right)^{2.4026}\\
&\approx 0.3567\ \text{kg}/\text{year}
\end{align*}
