Question

Shana is climbing a mountain at a constant pace. She rises in elevation by 17.5 feet per minute. After hiking for 30 minutes, a GPS app tells her that her elevation is 2,165 feet above sea level. Write a linear function for Shana's elevation, E, above sea level as a function of the time, t, she has been climbing in minutes.

Answer 1

Answer:

The linear equation for Shana's elevation is $E = 17.5\cdot t+1640$.

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:

$E = h_{o}+\dot h\cdot t$ (Eq. 1)

Where:

$h_{o}$ - Initial height above sea level, measured in feet.

$E$ - Elevation above sea level, measured in feet.

$\dot h$ - Climbing rate, measured in feet per minute.

$t$ - Time, measured in minutes.

If we know that $E = 2165\,ft$, $\dot h = 17.5\,\frac{ft}{min}$ and $t = 30\,s$. the initial height above sea level is:

$h_{o} = E - \dot h\cdot t$

$h_{o} = 2165\,ft-\left(17.5\,\frac{ft}{min} \right)\cdot (30\,min)$

$h_{o} = 1640\,ft$

The linear equation for Shana's elevation is $E = 17.5\cdot t+1640$.