Answer:
![y(t)=(-90\frac{feet}{minute})t+2000feet](https://tex.z-dn.net/?f=y%28t%29%3D%28-90%5Cfrac%7Bfeet%7D%7Bminute%7D%29t%2B2000feet)
Step-by-step explanation:
Given the linear function in the form
![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
We are going to represent the situation using the linear function.
We are going to call the variable ''x'' time. We can write x = t ⇒
![y=mt+b](https://tex.z-dn.net/?f=y%3Dmt%2Bb)
will be the altitude function that depends on the variable ''t'' that is time in minutes.
In the instant
the hot air balloon has an altitude of 2000 feet ⇒
⇒ ![b=2000feet](https://tex.z-dn.net/?f=b%3D2000feet)
We can think that the slope ''m'' is the constant rate of the function.
Given that the hot air balloon descends,
⇒![m=-90\frac{feet}{minute}](https://tex.z-dn.net/?f=m%3D-90%5Cfrac%7Bfeet%7D%7Bminute%7D)
Now we write the function :
![y=mt+b\\](https://tex.z-dn.net/?f=y%3Dmt%2Bb%5C%5C)
![y(t)=(-90\frac{feet}{minute})t+2000feet](https://tex.z-dn.net/?f=y%28t%29%3D%28-90%5Cfrac%7Bfeet%7D%7Bminute%7D%29t%2B2000feet)
For example, when t = 0 ⇒
![y(0)=(-90\frac{feet}{minute}).0+2000feet=2000feet](https://tex.z-dn.net/?f=y%280%29%3D%28-90%5Cfrac%7Bfeet%7D%7Bminute%7D%29.0%2B2000feet%3D2000feet)
Or if we want to find the time when the hot air balloon finally descends :
![0=(-90\frac{feet}{minute})t+2000feet](https://tex.z-dn.net/?f=0%3D%28-90%5Cfrac%7Bfeet%7D%7Bminute%7D%29t%2B2000feet)
![t=\frac{-2000feet}{-90\frac{feet}{minute}}=22.222minutes](https://tex.z-dn.net/?f=t%3D%5Cfrac%7B-2000feet%7D%7B-90%5Cfrac%7Bfeet%7D%7Bminute%7D%7D%3D22.222minutes)