To determine which table of values correctly represents the function [tex]\( s(t) = -4.9 t^2 + 19.6 t + 58.8 \)[/tex], we need to evaluate the given function at several specific points in time [tex]\( t \)[/tex].
Here's how the function behaves at the specified times:
Step-by-Step Calculation for Each [tex]\( t \)[/tex]:
1. At [tex]\( t = 0 \)[/tex]:
[tex]\[
s(0) = -4.9(0)^2 + 19.6(0) + 58.8 = 58.8
\][/tex]
So, [tex]\( s(0) = 58.8 \)[/tex].
2. At [tex]\( t = 1 \)[/tex]:
[tex]\[
s(1) = -4.9(1)^2 + 19.6(1) + 58.8 = -4.9 + 19.6 + 58.8 = 73.5
\][/tex]
So, [tex]\( s(1) = 73.5 \)[/tex].
3. At [tex]\( t = 2 \)[/tex]:
[tex]\[
s(2) = -4.9(2)^2 + 19.6(2) + 58.8 = -19.6 + 39.2 + 58.8 = 78.4
\][/tex]
So, [tex]\( s(2) = 78.4 \)[/tex].
4. At [tex]\( t = 3 \)[/tex]:
[tex]\[
s(3) = -4.9(3)^2 + 19.6(3) + 58.8 = -44.1 + 58.8 + 58.8 = 73.5
\][/tex]
So, [tex]\( s(3) = 73.5 \)[/tex].
5. At [tex]\( t = 4 \)[/tex]:
[tex]\[
s(4) = -4.9(4)^2 + 19.6(4) + 58.8 = -78.4 + 78.4 + 58.8 = 58.8
\][/tex]
So, [tex]\( s(4) = 58.8 \)[/tex].
6. At [tex]\( t = 5 \)[/tex]:
[tex]\[
s(5) = -4.9(5)^2 + 19.6(5) + 58.8 = -122.5 + 98 + 58.8 \approx 34.3
\][/tex]
So, [tex]\( s(5) \approx 34.3 \)[/tex].
Based on these evaluations, the correct table of values is:
[tex]\[
\begin{tabular}{|c|c|}
\hline
$t$ & $s(t)$ \\
\hline
0 & 58.8 \\
\hline
1 & 73.5 \\
\hline
2 & 78.4 \\
\hline
3 & 73.5 \\
\hline
4 & 58.8 \\
\hline
5 & 34.3 \\
\hline
\end{tabular}
\][/tex]
Clearly, neither of the provided tables matches the correct values. Therefore, the correct table is not among the options given.
