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 need to break down the problem using the concepts of linear functions:

1. Initial Amount: The pool starts with 600 gallons of water. This is your initial amount.

2. Rate of Change: The pool is draining at the rate of 100 gallons per hour. This indicates that for every hour that passes, the number of gallons in the pool decreases by 100 gallons. The rate of change can be represented as a negative value because the volume of water is decreasing. Therefore, the rate of change is -100 gallons per hour.

Putting that all together:

• Initial Amount: 600 gallons
• Rate of Change: -100 gallons per hour

The linear function that represents the amount of water \( g(t) \) in the pool at time \( t \) (in hours) can be written as:

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

where:

• \( g(t) \) is the number of gallons of water in the pool at time \( t \).
• \( 600 \) is the initial amount of water.
• \( -100 \) is the rate at which the pool is draining.

As time increases, the number of gallons decreases linearly according to this function.