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\begin{tabular}{|c|c|}
\hline
Time [tex]$(t)$[/tex] & Elevation [tex]$(e)$[/tex] \\
\hline
-2 & [tex]$a$[/tex] \\
\hline
3.5 & [tex]$b$[/tex] \\
\hline
30 & [tex]$c$[/tex] \\
\hline
\end{tabular}

Rory is staying in a cabin on a hill 300 feet above sea level. She walks down the hill to the water's edge. The equation of her average change in elevation over time is [tex]$e=300-10t$[/tex], where [tex]$t$[/tex] is the time in minutes since she left the cabin, and [tex]$e$[/tex] is her elevation with regard to sea level.

Which values are viable points, and what are their values in the table relating [tex]$t$[/tex] and [tex]$e$[/tex]?

[tex]\[
\begin{array}{l}
a = \square \\
b = \square \\
c = \square
\end{array}
\][/tex]



Answer :

GinnyAnswer
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]

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