Let's fill in the chart step-by-step:
First, let's correct the mismatched distances in the table. We'll use the expression \(16 t^2\) to calculate the distance fallen for each given time \(t\) and match it to the correct value.
1. For \( t = 0 \) seconds:
[tex]\[ 16 t^2 = 16 \times 0^2 = 16 \times 0 = 0 \text{ feet} \][/tex]
So, the distance for \( t = 0 \) should be 0 feet.
2. For \( t = 2 \) seconds:
[tex]\[ 16 t^2 = 16 \times 2^2 = 16 \times 4 = 64 \text{ feet} \][/tex]
So, the distance for \( t = 2 \) should be 64 feet.
3. For \( t = 4 \) seconds:
[tex]\[ 16 t^2 = 16 \times 4^2 = 16 \times 16 = 256 \text{ feet} \][/tex]
So, the distance for \( t = 4 \) should be 256 feet.
Let's update the chart with the correctly computed distances:
[tex]\[
\begin{tabular}{cc}
\hline
\begin{tabular}{c}
Time \( t \) \\
(in seconds)
\end{tabular}
&
\begin{tabular}{c}
Distance \( 16 t^2 \) \\
(in feet)
\end{tabular} \\
\hline
0 & 0 \\
2 & 64 \\
4 & 256 \\
\hline
\end{tabular}
\][/tex]
