Answer
a) $y=2.35x^3$
b) $y= 1203.20$
Work Step by Step
Since $y$ varies directly with $x^3$, we can write
\begin{equation}
y= kx^3,
\end{equation} where $k$ is the constant of proportionality that must be determined.
a) Given that $y= 150.4$ when $x= 4$, we can use this information to find $k$ as follows: \begin{equation}
\begin{aligned}
150.4&= 4^3k\\
\frac{150.4}{64}&=k\\
\therefore k&= 2.35.
\end{aligned}
\end{equation} The required model is
\begin{equation}
y= 2.35x^3.
\end{equation} b) Determine $y$ when $x=8$:
\begin{equation}
y= 2.35\cdot 8^3= 1203.20.
\end{equation} The answer is $y= 1203.20$ when $x= 8$.
