Answer
$5$ years
Work Step by Step
Given \begin{equation}
W(a)=22.37 \sqrt[5]{a^3}.
\end{equation} Set $W(a)= 60$ and solve for $a$.
\begin{equation}
\begin{aligned}
22.37 \sqrt[5]{a^3}& =60\\
\sqrt[5]{a^3}&=\frac{60}{22.37}\\
\left( a^{\frac{3}{5}} \right)^{\frac{5}{3}}&=\left( 2.682164 \right)^{\frac{5}{3}}\\
a&\approx 5.2.
\end{aligned}
\end{equation} The estimated age of a $60$ kilogram alpaca is about $5$ years.
