By: Sruthi Atluri, Isha Thakkar
Since the hot air balloon was sighted at an altitude of 800 feet and appears to be descending at a steady rate of 20 feet per minute, the function would be f(m) = 800-20m with m being minutes.
Since the second hot air balloon was sighted at 1200 feet, and was descending at 20 feet per minute, the function for this situation would be, f(m)=1200-20m with m being minutes. This balloon takes 60 minutes to land, which is 20 minutes longer than the first balloon. On the graph, the first balloon's line's x-intercept is 40. While the x-intercept of the second balloon is 60. This means that it takes the second balloon longer than the first to land.
Since the third balloon was sighted at 800 feet and is descending at 30 feet per minute, the function would be f(m)=800-30m with m being minutes. This balloon takes about 27 minutes to land, which is 13 minutes faster than the first balloon. Graphically, it shows that the x-intercept of the third balloon is about 29 and the x-intercept of the first balloon is 40. This shows that the third balloon is faster than the first balloon.
The fourth balloon is launched in the air at the same time the first balloon is sighted. It rises at a rate of 30 feet per minute. A function for this situation is f(m) = 30m. The first and fourth balloon are the same altitude after 16 minutes at 450 feet. Graphically, this means the point of intersection.
The third balloon would have to start its descent at the altitude of 1200 feet, so that it would reach the ground at the same time as the first balloon. The equation for this is y=1200-30x.