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Giải bài 2.26 trang 39 sách bài tập toán 11 - Kết nối tri thức với cuộc sống

Các bệnh truyền nhiễm có thể lây lan rất nhanh. Giả sử có năm người bị bệnh trong tuần đầu tiên của một đợt dịch, và mỗi người bệnh sẽ lây bệnh cho bốn người vào cuối tuần tiếp theo.

🌌Tổng hợp đề thi học kì 2 lớp 11 tất cả các môn - Kết nối tri thức

Toán - Văn - Anh - Lí - Hóa - Sinh
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Đề bài

Các bệnh truyền nhiễm có thể lây lan rất nhanh. Giả sử có năm người bị bệnh trong tuần đầu tiên của một đợt dịch, và mỗi người bệnh sẽ lây bệnh cho bốn người vào cuối tuần tiếp theo. Tính đến hết tuần thứ 10 của đợt dịch, có bao nhiêu người bị lây bởi căn bệnh này?

Phương pháp giải - Xem chi tiết

Cấp số nhân \(\left( {{u_n}} \right)\) có số hạng đầu là \({u_1}\) và công bội q thì số hạng tổng quát \({u_n}\) của nó được xác định bởi công thức \({u_n} = {u_1}.{q^{n - 1}}\) với \(n \ge 2\)

Lời giải chi tiết

Gọi \({u_n}\) là số người bị bệnh ở cuối tuần thứ n. Vì có năm người bị bệnh trong tuần đầu tiên của một đợt dịch, và mỗi người bệnh sẽ lây bệnh cho bốn người vào cuối tuần tiếp theo nên dãy số (\({u_n}\)) là một cấp số nhân với \({u_1} = 5\) và công bội \(q = 4.\) Suy ra, đến hết tuần thứ 10 của đợt dịch, số người bị lây bởi căn bệnh này là:\({u_{10}} = {u_1}.{q^9} = {5.4^9} = 1\;310\;720\) (người)

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Tham Gia Group Dành Cho Lớp 11 Chia Sẻ, Trao Đổi Tài Liệu Miễn Phí

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