Answer: The volume of water in the pool over time from when the hose is placed in the pool until the pool is full is defined by the equation [tex]V(t)=5000+1250t[/tex] and its graph is given below.
Explanation:
The total capacity of the pool is 20,000 gallon.
It is given that the pool contains 5000 gallons of water when a hose is placed in the pool and begins adding water at a rate of 1250 gallons per hour. So the initial volume of water is 5000.
Let the time is defined by t. So, the volume of water in the pool after time t is defined as,
[tex]V(t)=5000+1250t[/tex]
The capacity of the pool is 20,000 gallon, therefore the maximum value of V(t) is 20,000.
[tex]20,000=5000+1250t[/tex]
[tex]15000=1250t[/tex]
[tex]12=t[/tex]
The maximum value of t is 12, since the time is always positive, therefore we can say that,
[tex]0\leq t\leq 12[/tex]
The below graph representing the volume of water in the pool over time from when the hose is placed in the pool until the pool is full. The initial point is (0,5000) and the other point is (12,20000).
