To determine the correct equation that models the situation where a 28,000-gallon swimming pool is being drained by a pump at a rate of 700 gallons per hour, we need to understand the relationship between the amount of water remaining in the pool [tex]\( g \)[/tex] and the time [tex]\( t \)[/tex].
1. Initial condition:
- At [tex]\( t = 0 \)[/tex] (when the draining starts), the pool has 28,000 gallons of water. Thus, [tex]\( g = 28,000 \)[/tex].
2. Rate of draining:
- The pool loses 700 gallons each hour. This means that for each hour that passes, the number of gallons remaining in the pool decreases by 700 gallons.
To model this situation mathematically, we can set up an equation that describes how [tex]\( g \)[/tex] (the number of gallons remaining in the pool) decreases over time [tex]\( t \)[/tex] (the number of hours that have passed).
We can write:
[tex]\[ g = 28000 - 700t \][/tex]
This equation makes sense because:
- When [tex]\( t = 0 \)[/tex], [tex]\( g = 28000 \)[/tex], which represents the initial amount of water in the pool.
- For each hour [tex]\( t \)[/tex], [tex]\( g \)[/tex] decreases by 700 gallons, which is represented by the term [tex]\(- 700t \)[/tex].
So, the correct equation that models this situation is:
[tex]\[ g = 28000 - 700t \][/tex]
