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Bài 2.19 trang 56 SGK Toán 11 tập 1 - Cùng khám phá

Trực khuẩn E. Coli là loại vi khuẩn sinh sống trong đường tiêu hoá của người. Nó có lợi ích như ngăn chặn sự tấn công của vi khuẩn vào đường tiêu hóa, kích thích hệ miễn dịch của cơ thể và một số lợi ích khác, nhưng cũng là tác nhân gây bệnh tiêu chảy.
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Đề bài

Trực khuẩn E. Coli là loại vi khuẩn sinh sống trong đường tiêu hoá của người. Nó có lợi ích như ngăn chặn sự tấn công của vi khuẩn vào đường tiêu hóa, kích thích hệ miễn dịch của cơ thể và một số lợi ích khác, nhưng cũng là tác nhân gây bệnh tiêu chảy. Nó sinh sản theo hình thức phân bào. Trong điều kiện thích hợp thì cứ 20 phút, số tế bào E. Coli tăng gấp đôi. Nếu ban đầu có 1000 tế bào E. Coli, trong điều kiện thích hợp thị sau 5 giờ số tế bào E. Coli là bao nhiêu?

Phương pháp giải - Xem chi tiết

Từ đầu bài, xác định \({u_1},q,n\). Áp dụng công thức \({u_{n + 1}} = {u_1}.{q^n}\) để tính số tế bào sau 5 giờ.

Lời giải chi tiết

Gọi \({u_1}\) là số tế bào sau 20 phút đầu tiên \( \Rightarrow {u_1} = 1000.2 = 2000\).Cứ 20 phút thì số tế bào tăng gấp đôi. Ta lập được cấp số nhân với \( \Rightarrow q = 2\).Sau 5 giờ thì tế bào đã nhân đôi lần thứ 15 nên ta có số tế bào E.Coli là \({u_{15}} = {u_1}.{q^{14}} = {2000.2^{14}} = 32768000\) (tế bào).

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