Answer
$$
\kappa(t)=\frac{e^t}{\left(1+e^{2t}\right)^{3 / 2}},
$$
$$
\kappa(3)= \frac{e^3}{\left(1+e^{6}\right)^{3 / 2}},
$$
Work Step by Step
We have $$
\kappa(t)=\frac{\left|f^{\prime \prime}(t)\right|}{\left(1+f^{\prime}(t)^{2}\right)^{3 / 2}}=\frac{e^t}{\left(1+e^{2t}\right)^{3 / 2}},
$$
and hence
$$
\kappa(3)= \frac{e^3}{\left(1+e^{6}\right)^{3 / 2}},
$$
