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This problem involves exponential decay, where 3% of the water is draining every minute from a pool containing 1,500 gallons of water. Here's how we can approach the problem:

1. **Equation:**
   The water drains by 3% per minute, so the remaining water each minute is 97% of the previous amount. This gives us the exponential decay equation:
   \[
   W(t) = 1500 \times (0.97)^t
   \]
   where \( W(t) \) is the amount of water remaining after \( t \) minutes, and \( t \) is the time in minutes.

2. **Table (Values of water remaining over time):**

   Using the equation \( W(t) = 1500 \times (0.97)^t \), we can compute the values for \( t = 0, 1, 2, 3, 4, 5 \).

   | \( t \) (minutes) | \( W(t) \) (gallons) |
   |-------------------|----------------------|
   | 0                 | 1500                 |
   | 1                 | 1455                 |
   | 2                 | 1411.35              |
   | 3                 | 1368.01              |
   | 4                 | 1326.02              |
   | 5                 | 1285.24              |

3. **Domain:**
   Since the pool is draining, the domain would typically be all non-negative real numbers, \( t \geq 0 \), but practically it would stop when the water reaches 0 gallons.

4. **Graph:**
   To plot the graph, use a graphing tool like Desmos and enter the equation \( W(t) = 1500 \times (0.97)^t \). Label the x-axis as time in minutes and the y-axis as gallons of water.

   You should see a decreasing curve that approaches 0 as time increases, reflecting the exponential decay.

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### Five related questions:
1. How would the equation change if the draining rate was 5% instead of 3%?
2. What happens to the gallons of water after 10 minutes using this model?
3. How can you find the time when the pool is half-empty?
4. How does the initial amount of water affect the equation and the rate at which it drains?
5. How would the model change if the rate of water draining was not constant?

### Tip:
When modeling with exponential decay, always check the rate carefully—if it's a percentage, the base of the exponent is \( 1 - \text{rate} \).

At the end of the summer, I decided to drain the 1,500-gallon swimming pool. I noticed that it drains faster when there is more water in the pool. I found that 3% was draining out of the pool every minute. Use a table, a graph, and an equation to create a mathematical model of the gallons of water in the pool at t minutes.

Learn how to model the draining of a 1,500-gallon swimming pool with a 3% per minute decay rate. This problem involves creating an exponential decay equation, filling a data table, and plotting a graph to visualize the process. Suitable for high school students in Grades 9-12.

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