Answer:
The domain is all real values greater than or equal to 0 seconds and less than or equal to 40 seconds
The range is all real values greater than or equal to 0 feet and less than or equal to 2,000 feet
Step-by-step explanation:
Let
t ----> is the amount of time since the descent began
f(t) ---> is the height of a hot-air balloon descends
we know that
The linear equation in slope intercept form is equal to
![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
where
m is the unit rate or slope of the linear equation
b is the y-intercept or initial value
In this problem we have that
The slope or unit rate is equal to
---> is negative because is a decreasing function
The y-intercept or initial value is equal to
![b=2,000\ ft](https://tex.z-dn.net/?f=b%3D2%2C000%5C%20ft)
substitute
![f(t)=-50t+2,000](https://tex.z-dn.net/?f=f%28t%29%3D-50t%2B2%2C000)
The domain is the interval -----> [0,40]
![0\leq t\leq 40](https://tex.z-dn.net/?f=0%5Cleq%20t%5Cleq%2040)
All real values greater than or equal to 0 seconds and less than or equal to 40 seconds
The range is the interval ----> [0,2,000]
![0\leq f(t)\leq 2,000](https://tex.z-dn.net/?f=0%5Cleq%20f%28t%29%5Cleq%202%2C000)
All real values greater than or equal to 0 feet and less than or equal to 2,000 feet