To determine the equation that models the situation where a 28,000-gallon swimming pool is being drained using a pump that empties 700 gallons per hour, we need to analyze the given information step by step.
1. Initial Amount: The pool starts with 28,000 gallons of water. This is our initial condition before any drainage occurs.
2. Rate of Drainage: The pool is losing water at a rate of 700 gallons per hour. This means every hour, 700 gallons of water are removed from the pool.
3. Variables:
- [tex]\( g \)[/tex] represents the number of gallons of water remaining in the pool.
- [tex]\( t \)[/tex] represents the number of hours the pool has been draining.
4. Change in Water Volume: After [tex]\( t \)[/tex] hours, the total amount of water drained from the pool is [tex]\( 700 \times t \)[/tex] gallons. This is because the rate of 700 gallons per hour times the number of hours [tex]\( t \)[/tex] gives the total amount of water drained.
5. Remaining Water: To find the remaining water in the pool after [tex]\( t \)[/tex] hours, we subtract the drained water from the initial amount of 28,000 gallons.
Putting this all together, we can write the equation for the remaining water [tex]\( g \)[/tex] as follows:
[tex]\[ g = 28000 - 700 \times t \][/tex]
Therefore, the correct equation that models the number of gallons remaining in the pool after [tex]\( t \)[/tex] hours of draining is:
[tex]\[ g = 28000 - 700 \times t \][/tex]
So, out of the given options, the correct choice is:
[tex]\[ g = 28000 - 700 t \][/tex]
