# Hot Air Ballon Project

## What function relating the varibles best describes this situation?

f(x)=800-20x

The equation is saying that it starts at 800 and because it is decreasing, you subtract 20 times "x".

## Make graph to show the balloon's altitude every 5 minutes beginning at 5 minutes before the balloon was sighted until the balloon lands.

The graph shows the ballon going at a steady pace every five minutes and landing. It keeps a steady pace the whole time because the equation doesn't change.

## How high was the balloon 5 minutes before it was sighted? Explain.

You have to look at the pattern and see the rate it is going at. It goes at a rate of 20 feet per minute. 5 times 20 is 100 so the balloon would be at 900, 5 minutes before.

## A second balloon is first sighted at an altitude of 1200 feet but is descending at 20 feet per minute. Write the function that represents this situation. How much longer does it take for the second balloon to land compared with that of the first balloon? How does the descent of the balloons compare? Show the graph. Explain the relationship between the two lines.

function: f(x)=1200-20x

It takes a little bit longer because it starts higher and is going at the same pace. They end up crossing at 400 feet altitude.

## At the instant the first balloon is sighted, a fourth balloon is launched from the ground rising at a rate of 30 feet per minute. Write the function that represents this situation. When will the first and fourth balloon be at the same altitude? What is that altitude? Show the graph. What does this mean graphically?

Fourth Balloon: f(x)=800+30x

You have plus 30x because the balloon is going up not down. they cross at 800 feet altitude.

## At what altitude would the 3rd balloon have to begin its descent in order to reach the ground at the same time as the 1st balloon? What is the equation of the line?

It would have to descend at 20 feet per minute instead 30 so they would be at the same pace.