# Hot Air Balloon

### By Regan K and Jack T(Vanilla Thunder)

## Function

f(x)= 800- 20x

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

The balloon was at 900 feet 5 minutes before it was sighted, because if the balloon is decreasing at 20 feet per minute, 20(5) is 100. 100 plus 800 is 900.

## How long does it take for the balloon to reach an altitude of 20 feet?

It takes 40 minutes for the balloon to reach an altitude of 20 feet, because when plugged into the equation 800-20x, you get and altitude of 20 feet.

## Second Balloon

f(x)=1200-20x

It takes 60 minutes for the second balloon to land and 40 minutes for the first balloon to land. The second balloon lands 20 minutes after the first. The slopes are the same for the first and second balloon, because they are decreasing at different rates.

## Third Balloon

f(x)=800-30x

It takes 26.67 minutes for balloon to land. The difference between the second and first balloon are 33.33. The third balloon is decreasing at a faster rate, so the slope is steeper.

## Fourth Balloon

F(x)=30x

The first and fourth will be the same altitude at 480 feet, and 16 minutes. In the graph below the purple line represents the first balloon, and the red line represents the fourth balloon. The lines intersect at the cordinates, 16,480.

## Question 8

The third balloon would have to start at 1,200 feet to reach the ground at the same time as the first balloon. The equation is: y=1200-30(0)=x-30(40)