To determine the values of [tex]\(e\)[/tex] (elevation) for the given times [tex]\(t \)[/tex] in the table, we will use the equation of elevation, [tex]\( e = 300 - 10t \)[/tex]. Here are the detailed calculations:
1. For [tex]\( t = -2 \)[/tex]:
[tex]\[
e = 300 - 10(-2)
\][/tex]
Substituting [tex]\(-2\)[/tex] for [tex]\( t \)[/tex]:
[tex]\[
e = 300 + 20 = 320
\][/tex]
So, [tex]\( a = 320 \)[/tex].
2. For [tex]\( t = 3.5 \)[/tex]:
[tex]\[
e = 300 - 10(3.5)
\][/tex]
Substituting [tex]\( 3.5 \)[/tex] for [tex]\( t \)[/tex]:
[tex]\[
e = 300 - 35 = 265
\][/tex]
So, [tex]\( b = 265 \)[/tex].
3. For [tex]\( t = 30 \)[/tex]:
[tex]\[
e = 300 - 10(30)
\][/tex]
Substituting [tex]\( 30 \)[/tex] for [tex]\( t \)[/tex]:
[tex]\[
e = 300 - 300 = 0
\][/tex]
So, [tex]\( c = 0 \)[/tex].
Therefore, the values to fill in the table are:
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Time } (t) & \text{Elevation } (e) \\
\hline
-2 & 320 \\
\hline
3.5 & 265 \checkmark \\
\hline
30 & 0 \\
\hline
\end{array}
\][/tex]
And expressed individually:
[tex]\[
\begin{array}{l}
a = 320 \\
b = 265 \checkmark \\
c = 0
\end{array}
\][/tex]
