The following table shows the height at half-second intervals of a rock that breaks free from the top of a 390 -foot-tall cliff and falls without obstruction to the river below.
\begin{tabular}{|c|c|}
\hline Time $\boldsymbol{t}$ (in seconds) & Height $\boldsymbol{h}$ (in feet) \\
\hline 0 & 390 \\
\hline 0.5 & 386 \\
\hline 1.0 & 374 \\
\hline 1.5 & 354 \\
\hline 2.0 & 326 \\
\hline 2.5 & 290 \\
\hline 3.0 & 246 \\
\hline
\end{tabular}
Step 1 of 3 : The linear function of best fit that models the height of the rock after $t$ seconds is $h(t)=-48 t+410$. What is the linear-model height of the rock at time $t=0$ ? Round your answer to the nearest foot, if necessary.
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Final Answer: The linear-model height of the rock at time \(t=0\) is \(\boxed{410}\) feet.
Step 1 ：The question asks for the height of the rock at time \(t=0\) according to the linear model \(h(t)=-48 t+410\). To find this, we simply need to substitute \(t=0\) into the equation and solve for \(h(t)\).
Step 2 ：Substitute \(t=0\) into the equation: \(h_t = 410\)
Step 3 ：Final Answer: The linear-model height of the rock at time \(t=0\) is \(\boxed{410}\) feet.
