Using a linear function, it is found that it will take 118.7 seconds for the balloon to drop to below 310 feet.
What is a linear function?
A linear function is modeled by:
[tex]y = mx + b[/tex]
In which:
- m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
- b is the y-intercept, which is the value of y when x = 0.
In this problem:
- A hot-air balloon is 1200 feet off the ground, hence [tex]b = 1200[/tex].
- Its altitude is slowly changing at a constant rate of −7 1/2 feet per second, hence [tex]m = -7\frac{1}{2} = -7.5[/tex]
Then, the equation is:
[tex]y(t) = -7.5t + 1200[/tex]
It will drop below 310 feet when:
[tex]y(t) < 310[/tex]
Hence:
[tex]-7.5t + 1200 < 310[/tex]
[tex]-7.5t < -890[/tex]
[tex]7.5t > 890[/tex]
[tex]t > \frac{890}{7.5}[/tex]
[tex]t > 118.7[/tex]
It will take 118.7 seconds for the balloon to drop to below 310 feet.
You can learn more about linear functions at https://brainly.com/question/25823744
