Question

a group of climbers begin climbing at an elevation of 7000 feet and ascend at a steady rate of 500 vertical feet per hour. this situation can be modeled by a linear function. identify the independent and dependent variables. draw a graph of the function, then use the graph to find their elevation after 4 hours. is a linear model reasonable for this situation? the number of hours is the independent variable. the elevation in feet is the dependent variable. use the graphing tool to graph the line. the elevation after 4 hours is \\(\square\\) feet.

Explanation:

Step1: Identify the linear function

The initial elevation is 7000 feet, and the rate of ascent is 500 feet per hour. The linear function for elevation \( E \) (in feet) as a function of time \( t \) (in hours) is \( E(t) = 7000 + 500t \).

Step2: Calculate elevation at \( t = 4 \)

Substitute \( t = 4 \) into the function: \( E(4) = 7000 + 500 \times 4 \).
First, calculate \( 500 \times 4 = 2000 \).
Then, add to the initial elevation: \( 7000 + 2000 = 9000 \).

Answer:

9000