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

Now, use the rate of change and the initial amount to write an equation to represent the number of gallons of water in the pool as a function of time. Fill in the initial number of gallons of water that were in the pool.
t
g
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Time in hours
Gallons of water in the pool
Rate of change: -100
Initial amount: 600

Gallons of water in the pool = Initial number of gallons of water + Change in gallons
of water
g =
+

Answer 1

To represent the number of gallons of water in the pool as a function of time, we can set up the equation based on the initial amount of water and the rate of change due to the leak.

Let:

• \( g(t) \) = the number of gallons of water in the pool after \( t \) hours
• Initial amount = 600 gallons
• Rate of change = -100 gallons/hour (because the pool is losing water)

The change in gallons of water over time can be expressed as the rate of change multiplied by time:

\[ \text{Change in gallons} = \text{Rate of change} \times t = -100t \]

Now we can write the equation:

\[ g(t) = \text{Initial amount} + \text{Change in gallons} \]

Substituting the values we have:

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

This simplifies to:

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

So, the final equation that represents the number of gallons of water in the pool as a function of time \( t \) (in hours) is:

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