Longview rec center is filling up the outdoor pool at the beginning of summer. The number of gallons of water in the pool can be written as the function g(t)=10x, where t is the time in minutes what is the reasonable domain for this function?

Answer 1

To determine a reasonable domain for the function \( g(t) = 10t \), where \( g(t) \) represents the number of gallons of water in the pool and \( t \) is the time in minutes, we need to consider the context of filling a pool.

1. Starting Point: The filling of the pool begins at \( t = 0 \) minutes. This is the minimum value for \( t \).

2. Maximum Time: The maximum time will depend on how long it takes to fill the pool completely. If we assume there is a specific time (let's say \( T \) minutes) after which the pool is full, then the maximum value of \( t \) would be \( T \). However, since the problem does not provide a specific filling time, we can denote this maximum time as \( T \).

3. Reasonable Domain: Therefore, the reasonable domain for the function is all the values of \( t \) from 0 to \( T \) minutes, inclusively. In interval notation, this can be expressed as: \[ [0, T] \] where \( T \) is the time it takes to fully fill the pool.

If a specific time \( T \) is known for filling the pool, you can replace \( T \) with that value. For instance, if it takes 120 minutes to fill the pool, the domain would be \( [0, 120] \).