Final answer:
The domain of the function modeling the height of a hot-air balloon as it descends (f(m)=400-50m) is m ≥ 0, and the range is 0 ≤ f(m) ≤ 400, representing the height in feet from the moment of descent to when the balloon touches the ground.
Step-by-step explanation:
The function f(m)=400-50m models the height of a hot-air balloon, in feet, as it descends, where m is the number of minutes that have elapsed since the start of the descent. To determine the domain of this function, we must consider the physical context: the descent starts at m=0 and continues until the balloon lands. Since we don't know the exact moment the balloon lands, we will assume the descent continues for as long as it takes for the balloon to reach the ground, thus the domain is m ≥ 0. However, since we cannot have negative height, the function stops making physical sense once the height reaches zero.
The range of the function can be calculated from the equation: when m=0, f(m) is at its maximum height of 400 feet. As time passes, the balloon descends, meaning the height decreases until it reaches the ground. Thus, the range is the set of values the function f(m) can take, from 400 down to 0 feet, written as 0 ≤ f(m) ≤ 400.