This problem involves exponential decay, where the amount of oil in the tank decreases by 5% each hour. Let us solve it step by step.

Step 1: Define the formula for the amount of oil left in the tank

The amount of oil remaining in the tank after $t$ hours is given by the formula: $A(t) = A_0 \cdot (1 - r)^t$ where:

• $A_0 = 350$ gallons (initial amount of oil),
• $r = 0.05$ (leakage rate per hour, as a decimal),
• $t$ is the time in hours.

Step 2: Calculate the amount of oil remaining after 8 hours

Substitute the given values into the formula: $A(8) = 350 \cdot (1 - 0.05)^8 = 350 \cdot 0.95^8$

Using a calculator: $0.95^8 \approx 0.66342$ $A(8) \approx 350 \cdot 0.66342 = 232.197 \, \text{gallons}$

Step 3: Calculate the amount of oil that has leaked out

The amount of oil leaked out after 8 hours is: $\text{Leaked amount} = A_0 - A(8) = 350 - 232.197 \approx 117.803 \, \text{gallons}$

Step 4: Find the percentage of the original oil that has leaked

The percentage of oil leaked out is: $\text{Percent leaked} = \left( \frac{\text{Leaked amount}}{A_0} \right) \cdot 100$ $\text{Percent leaked} = \left( \frac{117.803}{350} \right) \cdot 100 \approx 33.66\%$

Final Answer:

After 8 hours, approximately 33.66% of the original 350 gallons has leaked out.

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Would you like further details or help with a related question? Here are some related queries:

1. What is the general behavior of exponential decay in terms of percentages?
2. How would the result change if the leak rate were different, e.g., 10% per hour?
3. How much oil remains after 12 hours?
4. What is the total oil leaked out after 24 hours?
5. How long will it take for half the oil to leak out (half-life)?

Tip: In exponential decay problems, always focus on the rate of change and how it compounds over time.