# Hot Air Balloon Project

### An investigation in hot air balloons descending over time

## 1. What is a Function Relation?

A function relation is a similarity in 2 different variables for a function. For example the function for the descending hot air balloon is Y= 800-20x. The function relation is is the descent of the balloon (or the altitude) and the time (or the feet per minute)

## 2. The Rate of the Balloon Descent

The rate of the descent of the balloon is how much the ballon goes down per minute. The first balloon's rate is 20 ft. per minute. If the interval is 5, the rate is 100 ft. per 5 minutes. 5 minutes before the balloon was sighted it was at 900 ft. Every 5 minutes after that it decreases 100 ft.

## 3. The Balloons Start!

The balloon was at 900 ft. 5 minutes before it started. According to the graph and the table the balloon starts at 800 ft. and the before the balloon starts it is at 900 ft. Each point on the graph is 100 less than the last one. This graph has a negative trend.

## 5. The Second Balloon Arrives!

The function is f(x)=1200-20x. This is basically the same as the first problem except the balloon is starting from a higher point. The graph shows this by both of the lines being parallel.

## 6. Three is a Crowd

f(x)=800-30x is the function for the new balloon. The new hot air balloon reaches the ground about 13 minutes earlier than the first. (13.5 to be exact) The 3rd balloon is going at a faster rate than the 1st one.

## 7. The Meet!

f(x)=30x is the function because every minute it is rising 30 ft. The 2 balloons meet at 16 minutes at an altitude of 480 feet. The point where the lines are intersecting is the point where the balloons are at the same altitude.

## 8. Every Thing Comes to an End

If both balloons were to reach at the same time balloon 3 would have to start at 1200 feet but go at the same rate as it was before. The blue line represents the 1st balloon (constant) and the green line represents the 3rd balloon starting at 1200 and going down 30 feet per minute. The equation is Y=1200-30x.