The Smiths are draining their 25,000 gallon swimming pool. It drains at a rate of 3,000 gallons an hour. Write a function that models the amount of water in the pool after t hours.
A) W = 25,000 - 3000t
Eliminate
B) W = 25,000 + 3000t
C) W = 3000 - 25,000t
D) W = 3000 + 25,000t
A is indeed correct, if you believe the model. In the real world, drain rate will depend on the amount of water left in the pool.
A is correct answer.
To determine the correct function that models the amount of water in the pool after t hours, we need to analyze the problem statement and understand the relationship between time and the amount of water drained.
According to the problem, the Smiths are draining their 25,000 gallon swimming pool at a constant rate of 3,000 gallons per hour. As time passes, the amount of water in the pool decreases.
Let's break down the given answer choices:
A) W = 25,000 - 3000t: This function represents the initial amount of water in the pool (25,000 gallons) minus the amount drained (3,000 gallons per hour multiplied by the number of hours t). This option seems reasonable based on the problem statement.
B) W = 25,000 + 3000t: This function represents the initial amount of water in the pool (25,000 gallons) plus the amount drained (3,000 gallons per hour multiplied by the number of hours t). However, since the Smiths are draining the pool, the amount of water should be decreasing, not increasing. Therefore, this option can be ruled out.
C) W = 3000 - 25,000t: This function represents the initial amount drained (3,000 gallons per hour) minus the amount of water in the pool (25,000 gallons multiplied by the number of hours t). This option does not accurately model the amount of water in the pool as it does not reflect the initial amount of water or the fact that water is being drained over time.
D) W = 3000 + 25,000t: This function represents the initial amount drained (3,000 gallons per hour) plus the amount of water in the pool (25,000 gallons multiplied by the number of hours t). Similar to option B, this option implies that the amount of water should be increasing, which is incorrect. Hence, this option can also be eliminated.
By process of elimination, the correct function that models the amount of water in the pool after t hours is:
A) W = 25,000 - 3000t