To solve this problem, we need to evaluate the elevation [tex]\(e\)[/tex] using the given equation [tex]\(e = 300 - 10t\)[/tex] for the specified time points [tex]\(t = -2\)[/tex], [tex]\(t = 3.5\)[/tex], and [tex]\(t = 30\)[/tex].
1. Calculate [tex]\( e \)[/tex] when [tex]\( t = -2 \)[/tex]:
- Substitute [tex]\( t = -2 \)[/tex] into the equation [tex]\(e = 300 - 10t\)[/tex]:
[tex]\[
e = 300 - 10(-2)
\][/tex]
- Simplify the expression:
[tex]\[
e = 300 + 20
\][/tex]
- Thus, the elevation [tex]\(e\)[/tex] when [tex]\( t = -2 \)[/tex] is:
[tex]\[
e = 320
\][/tex]
2. Calculate [tex]\( e \)[/tex] when [tex]\( t = 3.5 \)[/tex]:
- Substitute [tex]\( t = 3.5 \)[/tex] into the equation [tex]\(e = 300 - 10t\)[/tex]:
[tex]\[
e = 300 - 10(3.5)
\][/tex]
- Simplify the expression:
[tex]\[
e = 300 - 35
\][/tex]
- Thus, the elevation [tex]\(e\)[/tex] when [tex]\( t = 3.5 \)[/tex] is:
[tex]\[
e = 265.0
\][/tex]
3. Calculate [tex]\( e \)[/tex] when [tex]\( t = 30 \)[/tex]:
- Substitute [tex]\( t = 30 \)[/tex] into the equation [tex]\(e = 300 - 10t\)[/tex]:
[tex]\[
e = 300 - 10(30)
\][/tex]
- Simplify the expression:
[tex]\[
e = 300 - 300
\][/tex]
- Thus, the elevation [tex]\(e\)[/tex] when [tex]\( t = 30 \)[/tex] is:
[tex]\[
e = 0
\][/tex]
Now, we populate the table with the calculated values:
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Time } (t) & \text{Elevation } (e) \\
\hline
-2 & 320 \\
\hline
3.5 & 265.0 \\
\hline
30 & 0 \\
\hline
\end{array}
\][/tex]
Thus, the values in the table are:
[tex]\[
a = 320 \checkmark \\
b = 265.0 \checkmark \\
c = 0
\][/tex]
