1. **State the problem:** We want to determine if the number of weeks $t$ is proportional to the number of vehicles made $v$ when a factory makes 50 vehicles per week. 2. **Recall the definition of proportionality:** Two quantities $t$ and $v$ are proportional if there exists a constant $k$ such that $$v = k t$$ 3. **Given information:** The factory makes 50 vehicles per week. This means for each week $t$, the total vehicles made is $$v = 50 t$$ 4. **Check proportionality:** Since $v$ can be expressed as $v = 50 t$, $v$ is proportional to $t$. 5. **Find the constant of proportionality:** The constant $k$ is the number of vehicles made per week, which is $$k = 50$$ **Final answer:** Yes, $t$ is proportional to $v$, and the constant of proportionality is 50.