A swimming pool starts with 600 gallons of water in it. It springs a leak, and is draining at a rate of 100 gallons per hour.

Question

Start by finding the rate of change in this linear function. In other words, by how much does the number of gallons of water in the pool change for every hour?
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Time in hours
Gallons of water in the pool
Rate of change:

Initial amount: ?

Answer 1

To analyze the situation, we can express the number of gallons of water in the pool as a function of time, \(t\), in hours.

Given that the pool starts with 600 gallons and is draining at a rate of 100 gallons per hour, we can denote the amount of water in the pool after \(t\) hours with the function:

\[ g(t) = 600 - 100t \]

Where:

• \(g(t)\) is the number of gallons in the pool at time \(t\),
• 600 is the initial amount of water in the pool,
• 100 is the rate of change, which is how much the water decreases per hour,
• \(t\) is the time in hours.

Rate of Change:

The rate of change in this linear function is -100 gallons per hour (the negative sign indicates that the amount of water is decreasing).

Initial Amount:

The initial amount of water in the pool (when \(t = 0\)) is 600 gallons.

Summary:

• Rate of change: -100 gallons per hour (it decreases by 100 gallons for each hour)
• Initial amount: 600 gallons