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Bài 6 trang 60 SGK Toán 11 tập 1 - Chân trời sáng tạo

Một loại vi khuẩn được nuôi cấy trong phòng thí nghiệm, cứ mỗi phút số lượng lại tăng lên gấp đôi số lượng đang có. Từ một vi khuẩn ban đầu, hãy tính tổng số vi khuẩn có trong ống nghiệm sau 20 phút.

🏅Tổng hợp đề thi học kì 2 lớp 11 tất cả các môn - Chân trời sáng tạo

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

Một loại vi khuẩn được nuôi cấy trong phòng thí nghiệm, cứ mỗi phút số lượng lại tăng lên gấp đôi số lượng đang có. Từ một vi khuẩn ban đầu, hãy tính tổng số vi khuẩn có trong ống nghiệm sau 20 phút.

Phương pháp giải - Xem chi tiết

Sử dụng công thức số hạng tổng quát của cấp số nhân có số hạng đầu \({u_1}\) và công bội \(q\) thì số hạng tổng quát là: \({u_n} = {u_1}.{q^{n - 1}},n \ge 2\).

Lời giải chi tiết

Số lượng vi khuẩn trong ống nghiệm sau \(n\) phút là một cấp số nhân có số hạng đầu \({u_1} = 1\) và công bội \(q = 2\). Số lượng vi khuẩn ban đầu là \({u_1} = 1\). Số lượng vi khuẩn sau 1 phút là \({u_2}\). Số lượng vi khuẩn sau 2 phút là \({u_3}\). ... Số lượng vi khuẩn trong ống nghiệm sau 20 phút là: \({u_{21}} = {u_1}.{q^{n - 1}} = {1.2^{21 - 1}} = 1048576\) (vi khuẩn).

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