To solve the problem of modeling the draining of a 28,000-gallon swimming pool using a pump that removes 700 gallons per hour, let's carefully break down the situation and derive the equation step-by-step:
### Step-by-Step Solution:
1. Understanding Variables:
- Let [tex]\( g \)[/tex] represent the number of gallons remaining in the pool.
- Let [tex]\( t \)[/tex] represent the time in hours that the pool has been draining.
2. Initial Condition:
- The pool initially contains 28,000 gallons, so at [tex]\( t = 0 \)[/tex], [tex]\( g = 28,000 \)[/tex].
3. Rate of Change:
- The pool is draining at a rate of 700 gallons per hour.
4. Creating the Model:
- After 1 hour ([tex]\( t = 1 \)[/tex]), the pool will have 700 gallons less, so [tex]\( g \)[/tex] will be:
[tex]\[
g = 28000 - 700 \cdot 1 = 27300
\][/tex]
- After 2 hours ([tex]\( t = 2 \)[/tex]), the pool will have 1400 gallons less, so [tex]\( g \)[/tex] will be:
[tex]\[
g = 28000 - 700 \cdot 2 = 26600
\][/tex]
5. General Form:
- We observe a pattern that for any hour [tex]\( t \)[/tex], the number of gallons remaining [tex]\( g \)[/tex] can be expressed as:
[tex]\[
g = 28000 - 700 \cdot t
\][/tex]
### Conclusion:
The correct equation which models the given situation, where [tex]\( g \)[/tex] is the number of gallons remaining after [tex]\( t \)[/tex] hours, is:
[tex]\[ g = 28000 - 700 t \][/tex]
This matches answer choice:
[tex]\[ g = 28000 - 700 t \][/tex]
