Now, you need to record the change in the number of gallons, which you can find by multiplying the change in gallons per hour by the number of hours. Start by recording the change in gallons per hour.

Question

t
g
0
1
2
3
4
5
6
7
8
9
10
0
250
500
750
1,000
1,250
1,500
1,750
2,000
2,250
2,500
Time in hours
Gallons of water in the pool
Rate of change: 500
Initial amount: 250

Gallons of water in the pool = Initial number of gallons of water + Change in gallons
of water
g = 250 +
⋅
Change in gallons per hour

Answer 1

To calculate the change in gallons of water in the pool, you need to use the formula:

\[ \text{Gallons of water in the pool} , (g) = \text{Initial number of gallons of water} + (\text{Change in gallons per hour} \times \text{Time in hours}) \]

Given:

• Initial number of gallons = 250
• Change in gallons per hour = 500

You can rewrite the formula as:

\[ g = 250 + (500 \times t) \]

Where \( t \) represents the time in hours.

Now, let's calculate the gallons of water in the pool for each hour from 0 to 10:

For \( t = 0 \): \[ g = 250 + (500 \times 0) = 250 \]

For \( t = 1 \): \[ g = 250 + (500 \times 1) = 250 + 500 = 750 \]

For \( t = 2 \): \[ g = 250 + (500 \times 2) = 250 + 1000 = 1250 \]

For \( t = 3 \): \[ g = 250 + (500 \times 3) = 250 + 1500 = 1750 \]

For \( t = 4 \): \[ g = 250 + (500 \times 4) = 250 + 2000 = 2250 \]

For \( t = 5 \): \[ g = 250 + (500 \times 5) = 250 + 2500 = 2750 \]

For \( t = 6 \): \[ g = 250 + (500 \times 6) = 250 + 3000 = 3250 \]

For \( t = 7 \): \[ g = 250 + (500 \times 7) = 250 + 3500 = 3750 \]

For \( t = 8 \): \[ g = 250 + (500 \times 8) = 250 + 4000 = 4250 \]

For \( t = 9 \): \[ g = 250 + (500 \times 9) = 250 + 4500 = 4750 \]

For \( t = 10 \): \[ g = 250 + (500 \times 10) = 250 + 5000 = 5250 \]

Here’s a summary of the gallons in the pool at each hour:

| Time (hours) | Gallons of water in the pool | |--------------|-------------------------------| | 0 | 250 | | 1 | 750 | | 2 | 1250 | | 3 | 1750 | | 4 | 2250 | | 5 | 2750 | | 6 | 3250 | | 7 | 3750 | | 8 | 4250 | | 9 | 4750 | | 10 | 5250 |

This table shows the increase in the amount of water in the pool over the specified time period.