Question

An air balloon begins it's decent to the ground at 1000 ft above the ground and falls at a rate of 50 ft per minute. Select all that apply to this situation.

The slope is 1000 ft per minute. The balloon is falling at 1000 ft per minute.

The y-intercept is 50 ft. The balloon falls at a rate of 50 ft per minute.

The y-intercept is 1000 ft. The balloon begins to from an initial height of 1000 ft.


The slope is -50 ft per minute. The balloon is falling at 50 ft per minute.

It will take the balloon 20 minutes to reach the ground.

Answer 1

The correct options are 3, 4 and 5.

Explanation:

It is given that an air balloon begins it's decent to the ground at 1000 ft above the ground and falls at a rate of 50 ft per minute.

It means the initial height of air balloon is 1000. So, the y-intercept is (0,1000).

The ball falls at a rate of 50 ft per minute. So, the rate of change is

`m=-50`

The height of balloon is defined as

`h(x)=-50x+1000`
`[\because y=mx+b]`

Where, x is time in minutes.

The balloon will reach the ground when h(x)=0

`0=-50x+1000`

`50x=1000`

`x=20`

Therefore the options 3, 4 and 5 are correct.