9
QuizMultiple Choice

Convergent and Divergent Series

Question 9 • EA Pre-Calculus Credit Recovery

An underground storage container is leaking a toxic chemical. One year after the leak began, the chemical had spread 1500 meters from its source. After two years, the chemical had spread 900 meters more , and by the end of the third year, it had reached an additional 540 meters.If this pattern continues, how far will the spill have spread from its source after 10 years?

Answer
A
2775 meters
B
3750 meters
C
3727 meters
D
2940 meters

Explanation

The yearly increases form a geometric pattern: 1,500 meters, 900 meters, and 540 meters, with each increase equal to 0.6 times the previous one. The total distance after 10 years is the sum of the first 10 increases: 1,500 × (1 − 0.6¹⁰) ÷ (1 − 0.6) ≈ 3,727 meters. Therefore, the spill will have spread about 3,727 meters, choice c.

AI-written and checked against the verified answer.

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