# Hot-Air Balloon

## Question 1

The function that relates it the variables is F(x)= 800-20x

## Question 2

Table and Graph of balloons altitude every 5 minutes.

We started at -5 because that is 5 minutes before the balloon was sighted and we ended at 40 because that is when it lands

## Question 3

The balloon was 900 feet 5 minutes before it was sighted, because the balloon travels 100 feet every 5 minutes so if the ballon was at 800 feet when it was sighted, then 5 minutes before that it would have been 900 feet up.

## Question 4

The balloon will reach an altitude of 20 feet at 39 minutes and an will land at 40 minutes. It will land in 40 minutes because 800 divided by 20 is 40 and it will reach an altitude of 20 feet at 39 minutes because the balloon travels at a rate of 20 feet per minute so it will be a minute before it lands.

## Question 5

The function it represent the second balloon is f(x)= 1200-20x and the descent is longer than the first balloon because it takes 20 more minutes for the second balloon to land. The relationship between the two lines is that the second balloons line is not as the first balloons line since the second balloons descent is slower.

## Question 6

The function that represents the third balloon is f(x)=800-30x. The descent is faster than the first ballon, because it is 13 minutes shorter. The relationship between the two lines is that the third balloons line is steeper than the first balloons line because the descent was faster.

## Question 7

The function of the 4th ballon is f(x)=30x. The altitude where the first and 4th balloon will meet is 480 feet and they will meet at 16 minutes. Graphically this means that the two lines will intersect since they will be meeting at the same point.

## Question 8

For the 3rd balloon to reach the ground at the same time as the first balloon it would have to start at an altitude of 1200 feet. The equation of the line is f(x) = 1200-30x.

## Connections

In the 2nd question the graph is plotting the points in the table, and the explanation shows how 5 minutes before it was spotted is -5 on the graph.

In the 3rd question the text describing what us being shown on the graph.

In the 6th questions he graph is graphing the function.