Answer:
The linear equation for Shana's elevation is [tex]E = 17.5\cdot t+1640[/tex].
Step-by-step explanation:
According to the statement, we find that Shana is climbing at constant rate in time and height as a function of time can be represented by linear function:
[tex]E = h_{o}+\dot h\cdot t[/tex] (Eq. 1)
Where:
[tex]h_{o}[/tex] - Initial height above sea level, measured in feet.
[tex]E[/tex] - Elevation above sea level, measured in feet.
[tex]\dot h[/tex] - Climbing rate, measured in feet per minute.
[tex]t[/tex] - Time, measured in minutes.
If we know that [tex]E = 2165\,ft[/tex], [tex]\dot h = 17.5\,\frac{ft}{min}[/tex] and [tex]t = 30\,s[/tex]. the initial height above sea level is:
[tex]h_{o} = E - \dot h\cdot t[/tex]
[tex]h_{o} = 2165\,ft-\left(17.5\,\frac{ft}{min} \right)\cdot (30\,min)[/tex]
[tex]h_{o} = 1640\,ft[/tex]
The linear equation for Shana's elevation is [tex]E = 17.5\cdot t+1640[/tex].
