By: Pavan, Tyann, and Rye
The function of the first balloon's descending rate is F(x)=800-20x.
This graph shows that the first balloon is dropping at a steady rate of 20 feet per minute and 100 feet per 5 minutes. The x axis is the time after being sighted. and the y axis is the altitude of the ballon.
Five minutes before the ballon was sighted it was at 900 ft because 5 minutes before you see the balloon it would be 100 ft higher then 800 ft.
In this graph it shows that 5 minutes before it was sighted and the altitude of the balloon is 900 feet. It drops at a rate of 100 feet per 5 minutes and if it is dropping at the same rate then 5 minutes before it would have been sighted it would be 100 feet higher.
The ballon takes 39 minutes to reach 20 feet. It takes 40 minutes to land.
This graph shows that when x is 39 y is 20. So this means at 39 minutes the balloon will be at an altitude of 20 ft. The balloon will land in 40 minutes.
The function for the 2nd hot air balloon is F(x)=1200-20x. It will take the 2nd balloon 20 minutes longer to land. The descent for the first balloon will take less time because it starts at a lower altitude. The graph shows that the 1st balloon, which is the blue line, will land first. It also shows that the 2nd balloon, which is the purple line, will land after the 1st balloon.
The function for the 3rd balloons descent is 800-30x. The 3rd balloon will land before the 1st balloon because it has a larger rate of descent. The 3rd balloon has a rate increase of 10 ft/m compared to the 1st balloon. In the graph it shows that the 3rd balloon, which is the red line, will land before the first balloon which is the blue line.
The function for the 4th balloon is F(x)=30x. Both balloons will be at the same altitude at 16 minutes. That altitude is 480 ft. The point (16,480) is where the 2 lines will intersect.
The altitude that the 3rd balloon will have to start in order to land with the first balloon is 1200 ft. The equation is 1200-30x