Question

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 \( [0, 120] \).