A 20,000 gallon swimming pool contains 5000 gallons of water when a hose is placed in the pool and begins adding water at a rate of 1250 gallons per hour.

Question

Use the Segment tool to plot a graph representing the volume of water in the pool over time from when the hose is placed in the pool until the pool is full.

Keyboard Instructions
Initial graph state
The horizontal axis goes from -1.5 to 13.4 with ticks spaced every 1 unit(s).
The vertical axis goes from -1000 to 22000 with ticks spaced every 1000 unit(s).
Volume of Water in Pool
Time (h)Water in Pool (gal)

Answer 1

To plot the graph representing the volume of water in the swimming pool over time, we must define the parameters and equations for our situation.

Variables

• Initial volume of water in the pool (V0): 5000 gallons
• Rate of water being added (R): 1250 gallons per hour
• Total volume of the pool (Vmax): 20,000 gallons

Equation

The volume of water in the pool over time can be expressed with a linear function: \[ V(t) = V0 + R \cdot t \] where \( V0 = 5000 \) gallons, \( R = 1250 \) gallons/hour, and \( t \) is the time in hours.

Finding the Time to Fill the Pool

We can determine how long it will take to fill the pool completely by setting \( V(t) \) equal to \( Vmax \): \[ 20,000 = 5000 + 1250 \cdot t \] Subtract 5000 from both sides: \[ 15,000 = 1250 \cdot t \] Now, divide by 1250: \[ t = \frac{15,000}{1250} = 12 \text{ hours} \]

Points for the Graph

Now we can calculate the volume of water in the pool at various time intervals until it reaches capacity:

• At t = 0 hours: \[ V(0) = 5000 + 1250 \cdot 0 = 5000 \text{ gallons} \]

• At t = 1 hour: \[ V(1) = 5000 + 1250 \cdot 1 = 6250 \text{ gallons} \]

• At t = 2 hours: \[ V(2) = 5000 + 1250 \cdot 2 = 7500 \text{ gallons} \]

• At t = 3 hours: \[ V(3) = 5000 + 1250 \cdot 3 = 8750 \text{ gallons} \]

• At t = 4 hours: \[ V(4) = 5000 + 1250 \cdot 4 = 10000 \text{ gallons} \]

• At t = 5 hours: \[ V(5) = 5000 + 1250 \cdot 5 = 11250 \text{ gallons} \]

• At t = 6 hours: \[ V(6) = 5000 + 1250 \cdot 6 = 12500 \text{ gallons} \]

• At t = 7 hours: \[ V(7) = 5000 + 1250 \cdot 7 = 13750 \text{ gallons} \]

• At t = 8 hours: \[ V(8) = 5000 + 1250 \cdot 8 = 15000 \text{ gallons} \]

• At t = 9 hours: \[ V(9) = 5000 + 1250 \cdot 9 = 16250 \text{ gallons} \]

• At t = 10 hours: \[ V(10) = 5000 + 1250 \cdot 10 = 17500 \text{ gallons} \]

• At t = 11 hours: \[ V(11) = 5000 + 1250 \cdot 11 = 18750 \text{ gallons} \]

• At t = 12 hours: \[ V(12) = 5000 + 1250 \cdot 12 = 20000 \text{ gallons} \]

Summary of Key Points for the Graph:

| Time (h) | Water in Pool (gallons) | |----------|--------------------------| | 0 | 5000 | | 1 | 6250 | | 2 | 7500 | | 3 | 8750 | | 4 | 10000 | | 5 | 11250 | | 6 | 12500 | | 7 | 13750 | | 8 | 15000 | | 9 | 16250 | | 10 | 17500 | | 11 | 18750 | | 12 | 20000 |

Plotting the Graph

To plot this, set the x-axis (Time in hours) from 0 to 12 and the y-axis (Volume in gallons) from 5000 to 20000. The points will linearly connect from (0, 5000) to (12, 20000), creating a straight line.

Answer 2

tell me in bold words where to mark it

Answer 3

Certainly! Here’s how to label the axes and where to mark the points in bold:

Graph Properties

• Horizontal Axis (X-axis): Time (h)

  • Range: 0 to 12
  • Mark Ticks at: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12

• Vertical Axis (Y-axis): Water in Pool (gallons)

  • Range: 5000 to 20000
  • Mark Ticks at: 5000, 6250, 7500, 8750, 10000, 11250, 12500, 13750, 15000, 16250, 17500, 18750, 20000

Key Points to Mark on the Graph

• (0, 5000)
• (1, 6250)
• (2, 7500)
• (3, 8750)
• (4, 10000)
• (5, 11250)
• (6, 12500)
• (7, 13750)
• (8, 15000)
• (9, 16250)
• (10, 17500)
• (11, 18750)
• (12, 20000)

Final Instructions

• Connect all the points with a straight line to show the increase in water volume over time. This will create a linear graph from the starting point (0, 5000) to the endpoint (12, 20000).