Problem
2. In a pond, the area that is covered by algae doubles each week. When the algae was first spotted, the area it covered was about 12.5 square meters. a. Find the area, in square meters, covered by algae 10 days after it was spotted. Show your reasoning. b. Explain why we can find the area covered by algae 1 day after it was spotted by multiplying 12.5 by \( \sqrt[7]{2} \)
Solution
Step 1 ：Let \(A_n\) be the area covered by algae after \(n\) days.
Step 2 ：Since the area doubles each week (7 days), \(A_n = 12.5 * 2^{\frac{n}{7}}\).
Step 3 ：For 10 days, compute \(A_{10} = 12.5 * 2^{\frac{10}{7}} = 12.5 * 2^{1.4286} \approx 27.7275\) square meters.
