# Hot-Air Balloon

## 1.

A hot-air balloon is seen at 800 feet and is going down at a rate of about 20 feet per minute. Write a function to best describe this situation. f(x)=800-20x.

This works because when the balloon was sighted, it was at an altitude of 800 feet. So therefore, we have 800. Then it was seen going down at a rate of 20 feet per minute. That's we have 20x. When you plug in the amount of minutes in to x, then you can multiply that by 20 and then you get the height the balloon descended in x amount of minutes.

## 2.

In this problem, it is asking us the altitude of the balloon 5 minutes before it was spotted. It would still be 800-20x because if the original balloon was spotted at 0 minutes and if this was 5 minutes before, it would be negative 5.

## 3.

900 ft. This balloon was descending at a rate of 20 feet per minute, so then it means 5 minutes before it was sighted, it was 100 ft. higher.

## 4.

39 minutes. Every minute it is descending at a rate of 20 ft. In order for it to touch down, it has to descend 800 ft. If the balloon has 20 ft. remaining to touch down, then it has descended 780 ft.

## 5.

It would take 20 minutes longer. They relate because the rate of descend is the same. They will never collide with each other. This can also be proven by the graph because the lines are parallel.

## 6.

The third balloon lands 13.3 minutes earlier than the first because it is descending at a faster rate.These two lines will have the same y-intercept because they both were spotted at the same altitude.

## 7.

The first and fourth balloon will meet 16 minutes after decide and launch time. They will also meet at an alt. of 480 ft. When you simplify the equation down you get 800+50x. Then you divide 800 by 50 to get 16.

## 8.

The third balloon would have to begin its descent at 1200 ft. because when you use the equation y=mx+b, you have to simplify that to 0=?-30x. The x in this case would be 40 because that is when the first balloon touches down. The ? would be 1200. You would simplify that to 0=1200-(30)(40). That would be 0=1200-1200 which would finally be 0=0 which is the touch down altitude.