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 ----> Â 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
[tex]y=mx+b[/tex]
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
[tex]m=-\frac{2,000}{40}=-50\ feet\ per\ second[/tex] ---> is negative because is a decreasing function
The y-intercept or initial value is equal to
[tex]b=2,000\ ft[/tex]
substitute
[tex]f(t)=-50t+2,000[/tex]
The domain is the interval -----> [0,40]
[tex]0\leq t\leq 40[/tex]
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]
[tex]0\leq f(t)\leq 2,000[/tex]
All real values greater than or equal to 0 feet and less than or equal to 2,000 feet
