To solve this problem, we need to use the information provided about the height of the bleachers and the time it took for the baton to land. The baton was dropped from a height of 144 feet and landed after 3 seconds.
Let's find the height [tex]$h(t)$[/tex] at specific times using the given details:
1. At [tex]$t = 0$[/tex] seconds:
When Michael dropped the baton, it was at the top of the bleachers. The height at this moment, [tex]$h(0)$[/tex], is the initial height of the bleachers.
[tex]\[ h(0) = 144 \text{ feet} \][/tex]
2. At [tex]$t = 3$[/tex] seconds:
The baton landed on the ground after 3 seconds, so the height at this moment, [tex]$h(3)$[/tex], is 0 feet.
[tex]\[ h(3) = 0 \text{ feet} \][/tex]
Using this information, we can fill in the table:
[tex]\[
\begin{tabular}{|c|c|}
\hline
$t$ & $h(t)$ \\
\hline
0 & 144 \\
\hline
1 & 128 \\
\hline
2 & 80 \\
\hline
3 & 0 \\
\hline
\end{tabular}
\][/tex]
So, the complete table is:
[tex]\[
\begin{array}{|c|c|}
\hline
t & h(t) \\
\hline
0 & 144 \\
\hline
1 & 128 \\
\hline
2 & 80 \\
\hline
3 & 0 \\
\hline
\end{array}
\][/tex]
