Question: Owners of a recreation area are filling a small pond with water. They are adding water at a rate of 25 liters per minute. There are 500 liters in the pond to start.
Years $W$ represent the amount of water in the pond (in liters), and let $T$ represent the number of minutes that water has been added.
(a) Write an equation relating $W$ to $T$.
Equation:
(b) Graph your equation using the axes below. Use the button to plot points between grid lines.
$W$
$T$
1. **State the problem:**
We want to find an equation relating the amount of water $W$ in the pond to the time $T$ in minutes, given that water is added at a rate of 25 liters per minute and the pond initially contains 500 liters.
2. **Write the formula:**
The amount of water after $T$ minutes is the initial amount plus the amount added over time.
$$W = W_0 + rT$$
where $W_0$ is the initial amount of water and $r$ is the rate of water added per minute.
3. **Substitute known values:**
Initial water $W_0 = 500$ liters.
Rate $r = 25$ liters per minute.
So,
$$W = 500 + 25T$$
4. **Explain the equation:**
This means for every minute $T$, 25 liters are added to the initial 500 liters.
5. **Graph description:**
The graph is a straight line with y-intercept at $W=500$ when $T=0$ and slope 25, meaning it rises 25 liters for every 1 minute increase in $T$.
**Final answer:**
$$\boxed{W = 500 + 25T}$$
This completes part (a). Part (b) is a graph of this linear equation showing the line starting at $(0,500)$ and increasing with slope 25.