Problem
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. Answer Keyboard Shortcuts
Solution
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.
