2020-I-10

When $h = 3$, $P = 59$, we have

$\begin{array}{rcll}
59 & = & k_1 + k_2 (3)^3 \\
59 & = & k_1 + 27k_2 & \ldots \unicode{x2460}
\end{array}$

When $h=7$, $P=691$, we have

$\begin{array}{rcll}
691 & = & k_1 + k_2 (7)^3 \\
691 & = & k_1 + 343 k_2 & \ldots \unicode{x2461}
\end{array}$

$\unicode{x2461} – \unicode{x2460}$, we have

$\begin{array}{rcl}
632 & = & 316 k_2 \\
k_2 & = & 2
\end{array}$

Sub. $k_2 = 2$ into $\unicode{x2460}$, we have

$\begin{array}{rcl}
59 & = & k_1 + 27(2) \\
k_1 & = & 5
\end{array}$

Therefore, $P= 5 + 2h^3$.

The price of a brand $X$ souvenir of height $4 \text{ cm}$

$\begin{array}{cl}
= & 5 + 2(4)^3 \\
= & \$133
\end{array}$

$\begin{array}{cl}
= & 5 + 2(5)^3 \\
= & \$255
\end{array}$

The total price of $2$ brand $X$ souvenir of height $4 \text{ cm}$

$\begin{array}{cl}
= & 2 \times 133 \\
= & \$266
\end{array}$

Since $\$255 < \$266$, then the claim is not correct.