Question: Weather balloons are filled with hydrogen and released at various sites to measure and transmit data about conditions such as air pressure and temperature. A weather balloon is filled with hydrogen at the rate of 0.5 ft3/s. Initially, the balloon has 4 ft of hydrogen.
(a) Find a linear function $V$ that models the volume of hydrogen in the balloon at any time $t$.
1. **State the problem:** We need to find a linear function $V(t)$ that models the volume of hydrogen in the balloon at any time $t$ seconds.
2. **Understand the given information:**
- The balloon is initially filled with 4 ft³ of hydrogen.
- Hydrogen is added at a constant rate of 0.5 ft³/s.
3. **Recall the formula for linear functions:**
A linear function modeling volume over time can be written as:
$$V(t) = V_0 + rt$$
where $V_0$ is the initial volume and $r$ is the rate of change (rate of filling).
4. **Substitute the known values:**
- Initial volume $V_0 = 4$ ft³
- Rate $r = 0.5$ ft³/s
So,
$$V(t) = 4 + 0.5t$$
5. **Interpretation:**
This means at time $t=0$, the volume is 4 ft³, and for every second that passes, the volume increases by 0.5 ft³.
**Final answer:**
$$\boxed{V(t) = 4 + 0.5t}$$