Problem

Mr. Jackson is filling his family's pool for the summer. He's using a hose with a flow rate of 15 gallons per minute, and it takes him 120 minutes to fill the 1,800-gallon pool. The function $V(t)$ represents the volume of water in the pool, in gallons, $t$ minutes after Mr. Jackson starts filling it.

What is the domain of $V(t)$ ?
all whole numbers
all whole numbers from 0 to 120
all real numbers
all real numbers from 0 to 120
Submik

Answer

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Answer

\(\boxed{\text{The domain of } V(t) \text{ is all real numbers from 0 to 120.}}\)

Steps

Step 1 :The problem involves Mr. Jackson filling his family's pool with a hose that has a flow rate of 15 gallons per minute. It takes him 120 minutes to fill the 1,800-gallon pool. The function $V(t)$ represents the volume of water in the pool, in gallons, $t$ minutes after Mr. Jackson starts filling it.

Step 2 :The domain of a function is the set of all possible input values. In this case, the input value is the time in minutes.

Step 3 :Since Mr. Jackson starts filling the pool at time 0 and stops at 120 minutes, the domain of the function $V(t)$ should be all real numbers from 0 to 120.

Step 4 :This is because time is a continuous variable and can take any value in this interval.

Step 5 :\(\boxed{\text{The domain of } V(t) \text{ is all real numbers from 0 to 120.}}\)

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