Let’s go through the problem step by step.
Rory's elevation [tex]\( e \)[/tex] as a function of time [tex]\( t \)[/tex] is given by the equation:
[tex]\[ e = 300 - 10t \][/tex]
We need to find the values of [tex]\( e \)[/tex] for the given times [tex]\( t = -2 \)[/tex], [tex]\( t = 3.5 \)[/tex], and [tex]\( t = 30 \)[/tex].
### Calculation for [tex]\( t = -2 \)[/tex]:
Substitute [tex]\( t = -2 \)[/tex] into the equation [tex]\( e = 300 - 10t \)[/tex]:
[tex]\[
e = 300 - 10(-2) \\
e = 300 + 20 \\
e = 320
\][/tex]
So, for [tex]\( t = -2 \)[/tex], [tex]\( e = 320 \)[/tex].
### Calculation for [tex]\( t = 3.5 \)[/tex]:
Substitute [tex]\( t = 3.5 \)[/tex] into the equation [tex]\( e = 300 - 10t \)[/tex]:
[tex]\[
e = 300 - 10(3.5) \\
e = 300 - 35 \\
e = 265
\][/tex]
So, for [tex]\( t = 3.5 \)[/tex], [tex]\( e = 265 \)[/tex].
### Calculation for [tex]\( t = 30 \)[/tex]:
Substitute [tex]\( t = 30 \)[/tex] into the equation [tex]\( e = 300 - 10t \)[/tex]:
[tex]\[
e = 300 - 10(30) \\
e = 300 - 300 \\
e = 0
\][/tex]
So, for [tex]\( t = 30 \)[/tex], [tex]\( e = 0 \)[/tex].
### Filling in the table
We can now fill in the values for [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex] in the table:
[tex]\[
\begin{array}{|c|c|}
\hline \text{Time} (t) & \text{Elevation} (e) \\
\hline -2 & 320 \\
\hline 3.5 & 265 \\
\hline 30 & 0 \\
\hline
\end{array}
\][/tex]
Therefore, the values for the table are:
[tex]\[
a = 320 \\
b = 265 \checkmark \\
c = 0
\][/tex]
