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Giải câu hỏi mở đầu trang 20 SGK Toán 12 tập 1 - Kết nối tri thức

Giả sử khối lượng còn lại của một chất phóng xạ (gam) sau t ngày phân rã được cho bởi hàm số (mleft( t right) = 15{e^{ - 0,012t}}). Khối lượng m(t) thay đổi ra sao khi (t to + infty )? Điều này thể hiện trên Hình 1.18 như thế nào?

♛Tổng hợp đề thi học kì 2 lớp 12 tất cả các môn - Kết nối tri thức

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Đề bài

Giả sử khối lượng còn lại của một chất phóng xạ (gam) sau t ngày phân rã được cho bởi hàm số \(m\left( t \right) = 15{e^{ - 0,012t}}\). Khối lượng m(t) thay đổi ra sao khi \(t \to  + \infty \)? Điều này thể hiện trên Hình 1.18 như thế nào?

Phương pháp giải - Xem chi tiết

Sử dụng kiến thức về khái niệm tiệm cận ngang của đồ thị hàm số để tìm tiệm cận ngang: Đường thẳng \(y = {y_0}\) gọi là đường tiệm cận ngang (gọi tắt là tiệm cận ngang) của đồ thị hàm số \(y = f\left( x \right)\) nếu \(\mathop {\lim }\limits_{x \to  + \infty } f\left( x \right) = {y_0}\) hoặc \(\mathop {\lim }\limits_{x \to  - \infty } f\left( x \right) = {y_0}\).

Lời giải chi tiết

Ta có: \(\mathop {\lim }\limits_{t \to  + \infty } m\left( t \right) = \mathop {\lim }\limits_{t \to  + \infty } 15{e^{ - 0,012t}} = \mathop {\lim }\limits_{t \to  + \infty } \frac{{15}}{{{e^{0,012t}}}} = 0\). Do đó, \(m\left( t \right) \to 0\) khi \(t \to  + \infty \). Trong hình 1.18, khi \(t \to  + \infty \) thì m(t) càng gần trục hoành Ot (nhưng không chạm trục Ot).

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