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 9000 feet. a linear model dropdown reasonable.

Explanation:

Step1: Analyze the climbing situation

The climbers start at 7000 feet and ascend at 500 feet per hour. A linear model assumes a constant rate, and here the ascent rate is steady (constant), so the relationship between time (hours) and elevation (feet) is linear (elevation = 7000 + 500×time). There's no indication of the rate changing (e.g., fatigue, terrain changes aren't mentioned), so the linear model fits as the rate is constant.

Step2: Confirm linear model validity

Since the ascent rate is steady (500 feet per hour, constant), the elevation changes by a constant amount each hour. This matches the linear function's property of a constant slope (rate of change). So a linear model is reasonable.

Answer:

A linear model is reasonable.