# Hot-Air Balloon

## #1

f(x)=800-20x is the function for the first hot air balloon sighted.

## #2

The table below represents every 5 minutes when the balloon was sighted beginning at 5 minutes before it was sighted and its altitude in feet

## #3

The balloon was at 900 ft 5 minutes before it was sighted. On the graph it shows that at 900 ft it is at -5

The first balloon goes down at 20 ft per minute and reaches the ground at 40 min.

## #4

It takes 39 min for the balloon to be 20 ft from the ground. At 40 min, the balloon has landed. The balloon is then descending at a rate of 20 feet per minute. So at 39 minutes, it is 20 feet from the ground.

## #5

f(x)=1200- 20x is the second balloon's equation. The second balloon takes 20 more minutes and is always 400 ft higher than the first. They each go down 20 ft. each minute.

The first balloon, the red line goes down 20 ft. per second and hits the ground at 40 feet. The second balloon or blue line also goes down by 20 but starts 400 ft. higher at 1200. It hits the ground after 60 min.

## #6

f(x)=800-30x represents the third balloon. The first balloon takes about 13 more minutes and it descends ten ft. less each minute. Once the balloons are seen at 800 ft, the third balloon descends much faster than the first

The first balloon (blue line) goes down much slower than the third balloon (red line) which descends at 30 ft. per minute.

## #7

f(x)=30x is the 4th balloons equation. The fourth and 1st are at the same altitude after 16 min and will be at the same altitude of 480 ft. Graphically they intercept at 480 ft. and the coordinates are (16, 480)

The lines intersect at (16,480). The red line is the 4th balloon and the blue line is the 1st.

## #8

The 3rd balloon would start descending at 1200 ft and the first at 800 ft. for them to reach the ground at the same time. f(x)=1200-30x would be the third balloon equation. Because it is descending ten more feet per minute, they would hit the ground at the same time.