Given:
[tex]\begin{gathered} consant\text{ rate = }2.5\text{ gallons/min} \\ bucket\text{ size = }18\text{ gallon} \end{gathered}[/tex]
Let the time at which the bucket is filled be x
We can write:
At time t = 0 , Volume (V) = 0
At time t = x, Volume (V) = 18
Using the slope formula:
[tex]\begin{gathered} \text{slope = }\frac{V_{t=x}-V_{t=0}}{x-0} \\ \frac{18-0}{x-0}=\text{ 2.5} \end{gathered}[/tex]
Solving for x:
[tex]\begin{gathered} 2.5x\text{ = 18} \\ x\text{ = 7.2 min} \end{gathered}[/tex]
Recall that the domain of the function V is the time interval that satisfies the function.
Since the bucket becomes filled at 7.2min, the domain of the function V is:
[tex]0\text{ }\leq\text{ t }\leq\text{ 7.2 }[/tex]
Answer: Option A
