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

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

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\,(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\,(ft)/(min) \right)\cdot (30\,min)`

`h_(o) = 1640\,ft`

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