Subjects algebra

Water Volume 6C437F

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1. **State the problem:** We need to find the value of $V(4)$, which represents the amount of water in the tank after 4 minutes. 2. **Understand the graph:** The graph shows a straight line starting at about 120 liters at 0 minutes and rising to slightly above 510 liters at 19 minutes. This suggests a linear function of the form: $$V(x) = mx + b$$ where $m$ is the slope (rate of change of water per minute) and $b$ is the initial amount of water at time 0. 3. **Find the slope $m$:** Using the points $(0,120)$ and $(19,510)$, $$m = \frac{510 - 120}{19 - 0} = \frac{390}{19} = 20.5263$$ 4. **Find the equation:** Since $b = 120$, the function is: $$V(x) = 20.5263x + 120$$ 5. **Calculate $V(4)$:** $$V(4) = 20.5263 \times 4 + 120 = 82.1052 + 120 = 202.1052$$ 6. **Interpretation:** After 4 minutes, there are approximately 202 liters of water in the tank. **Final answer:** $$V(4) \approx 202$$ liters This means that after 4 minutes, the tank contains about 202 liters of water.