Subjects algebra

Water Leak Decay 9D4E09

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1. **State the problem:** A bucket initially contains 25 litres of water. It loses 12% of its water every minute due to a leak. We need to find the amount of water left after 10 minutes using the concept of compound decay. 2. **Formula used:** The amount remaining after compound decay is given by: $$ A = P \times (1 - r)^t $$ where: - $A$ is the amount after time $t$, - $P$ is the initial amount, - $r$ is the decay rate per time period (as a decimal), - $t$ is the number of time periods. 3. **Identify values:** - $P = 25$ litres - $r = 0.12$ (12% loss per minute) - $t = 10$ minutes 4. **Calculate:** $$ A = 25 \times (1 - 0.12)^{10} = 25 \times (0.88)^{10} $$ 5. **Evaluate:** Calculate $0.88^{10}$: $$ 0.88^{10} \approx 0.2785 $$ 6. **Final amount:** $$ A = 25 \times 0.2785 = 6.9625 $$ litres **Answer:** After 10 minutes, approximately **6.96 litres** of water remain in the bucket.