Question

A weather balloon is dropping at a rate of 4/3 miles per hour from an

initial height of 2 miles. If the balloon's height were graphed as a functio
of time, what would be the x-intercept?

Answer 1

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Answer 2

The x-intercept of the weather balloon's height function is approximately 1.5 hours.

The x-intercept represents the time when the height of the weather balloon is zero.

To find this, set the height function equal to zero and solve for time.

In this case, the height function is given by the equation:

h(t) = 2 −
`(4)/(3)`t.

Setting h(t) to zero gives:

0 = 2 -
`(4)/(3)`t,

Solving for t yields:

`(4)/(3)`t = 2 - 0

`(4)/(3)`t = 2

t = 2 x
`(3)/(4)` =
`(6)/(4)`

t≈1.5 hours

Therefore, the x-intercept occurs around 1.5 hours, indicating that after approximately 1.5 hours, the weather balloon will reach the ground, assuming a constant drop rate of 4/3 miles per hour from an initial height of 2 miles.