Giả sử doanh số (tính bằng số sản phẩm) của một sản phẩm mới (trong vòng một số năm nhất định) tuân theo quy luật logistic được mô hình hoá bằng hàm số \(y=f\left( t \right)=\frac{5\,000}{1+5{{\text{e}}^{-t}}},\,t\ge 0,\) trong đó thời gian \(t\) (năm) được tính kể từ khi phát hành sản phẩm mới. Khi đó, đạo hàm \(f\text{ }\!\!'\!\!\text{ }\left( t \right)\) sẽ biểu thị tốc độ bán hàng. Sau khi phát hành bao nhiêu năm thì tốc độ bán hàng là lớn nhất? (làm tròn kết quả tới chữ số hàng phần mười).
Hãy suy nghĩ và trả lời câu hỏi trước khi xem đáp án
Ta có: \(f\text{ }\!\!'\!\!\text{ }\left( t \right)=\frac{-5\,000\left( 1+5{{\text{e}}^{-t}} \right)}{{{\left( 1+5{{\text{e}}^{-t}} \right)}^{2}}}=\frac{25\,000{{\text{e}}^{-t}}}{{{\left( 1+5{{\text{e}}^{-t}} \right)}^{2}}}\)
Tốc độ bán hàng là lớn nhất khi \(f\text{ }\!\!'\!\!\text{ }\left( t \right)\) lớn nhất.
Đặt \(h\left( t \right)=\frac{25\,000{{\text{e}}^{-t}}}{{{\left( 1+5{{\text{e}}^{-t}} \right)}^{2}}}\).
\(\begin{align} & h\text{ }\!\!'\!\!\text{ }\left( t \right)=\frac{-25\,000{{\text{e}}^{-t}}{{\left( 1+5{{\text{e}}^{-t}} \right)}^{2}}-2.\left( -5{{\text{e}}^{-t}} \right).\left( 1+5{{\text{e}}^{-t}} \right).25\,000{{\text{e}}^{-t}}}{{{\left( 1+5{{\text{e}}^{-t}} \right)}^{4}}} \\ & =\frac{-25\,000{{\text{e}}^{-t}}\left( 1+5{{\text{e}}^{-t}} \right)\left( 1+5{{\text{e}}^{-t}}-10{{\text{e}}^{-t}} \right)}{{{\left( 1+5{{\text{e}}^{-t}} \right)}^{4}}}=\frac{-25\,000{{\text{e}}^{-t}}\left( 1-5{{\text{e}}^{-t}} \right)}{{{\left( 1+5{{\text{e}}^{-t}} \right)}^{3}}} \\ \end{align}\)
\(h\text{ }\!\!'\!\!\text{ }\left( t \right)=0\Leftrightarrow \frac{-25\,000{{\text{e}}^{-t}}\left( 1-5{{\text{e}}^{-t}} \right)}{{{\left( 1+5{{\text{e}}^{-t}} \right)}^{3}}}=0\Leftrightarrow 1-5{{\text{e}}^{-t}}=0\Leftrightarrow {{\text{e}}^{-t}}=\frac{1}{5}\Leftrightarrow t=\text{ln}5\)
(thỏa mãn)
Lập bảng biến thiên với \(t\in \left[ 0;+\infty \right)\):
Vậy sau khi phát hành khoảng \(\text{ln}5\approx 1,6\) năm thì thì tốc độ bán hàng là lớn nhất.
Bộ Đề Kiểm Tra Giữa Học Kì I - Toán 12 - Chân Trời Sáng Tạo là tài liệu ôn luyện toàn diện và hữu ích, giúp học sinh lớp 12 củng cố kiến thức, phát triển kỹ năng giải toán chuyên sâu. Được thiết kế với cấu trúc câu hỏi đa dạng, bám sát nội dung chương trình học, đề thi không chỉ rèn luyện khả năng tư duy logic mà còn khuyến khích học sinh phân tích, vận dụng kiến thức một cách linh hoạt và sáng tạo. Đây là hành trang vững chắc, giúp các em tự tin đối mặt với kỳ thi, đạt được thành tích tốt nhất và xây dựng nền tảng Toán học bền vững cho các chặng đường học tập tiếp theo.
Câu hỏi liên quan
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Nhiều nhà văn, nhà thơ lớn đã xuất hiện ở Pháp vào thế kỉ:
Nhiều quốc gia trên thế giới áp dụng biện pháp đánh thuế suất cao đối với một số hàng hoá, dịch vụ đặc biệt, nhằm điều tiết việc sản xuất và tiêu dùng xã hội cũng như nhập khẩu hàng hóa, từ đó tăng nguồn thu cho ngân sách nhà nước là thực hiện loại thuế nào sau đây?
CHỦ ĐỀ: TÁC ĐỘNG CỦA SUY THOÁI KINH TẾ ĐẾN SẢN XUẤT KINH DOANH CỦA CÁC DOANH NGHIỆP Ở MỘT SỐ TỈNH PHÍA BẮC
(Tham khảo bài văn của chủ đề trong đường link dưới đây ở trang 21)
https://tvsthpt.dlib.vn/app/doc-sach-ebook/d00b996754ec
Và trả lời câu hỏi sau:
Thông tin nào sau đây KHÔNG được đề cập đến trong văn bản?
Xuất phát giá trị đầu vào là số nguyên dương \(N\), thuật toán \(P\) được tiến hành như sau:
1. Tính tổng các chữ số của \(N\) để thu được \({{N}_{1}}\);
2. Tính tổng các chữ số của \({{N}_{1}}\) để thu được \({{N}_{2}}\);
3. Cứ như vậy cho đến lúc giá trị của các \({{N}_{k}}\) không thay đổi nữa thì dừng lại và ghi kết quả làm giá trị đầu ra \(\text{P}\left( \text{N} \right)\).
Ví dụ với \(\text{N}=883743746\), \({{N}_{1}}=8+8+3+7+4+3+7+4+6=50\), \({{N}_{2}}=5+0=5\), \({{N}_{3}}=5\), do vậy giá trị đầu ra \(\text{P}\left( 883743746 \right)\) bằng 5.
Điền số tự nhiên vào chỗ trống để hoàn thiện
Câu sau:
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Để nhập từ bàn phím biến a kiểu nguyên ta viết:
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Trong thông tin liên lạc bằng sóng vô tuyến, mạch tách sóng ở máy thu thanh có tác dụng
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Những hành vi nào vi phạm pháp luật trong sử dụng Tin học?
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Diều ở các loài động vật thuộc lớp chim được hình thành từ bộ phận nào của ống tiêu hoá?
Read the following passage about home schooling in the UK and mark the letter A, B, C or D on your answer sheet to indicate the best answer to each of the following questions from 23 to 30.
Full-time education in the UK is compulsory from the age of five to sixteen, but this doesn’t have to be in a school. Around 50,000 children are educated at home. This is called ‘homeschooling’.
Parents take their children out of school for different reasons, like illness and the need for special care, or because the distance to the nearest school may be too far. Some children are simply unhappy at school. Whatever the reason, they’re allowed to study at home, although inspectors regularly check how they are getting on.
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The family’s home is in a remote part of Wales. ‘The girls were fine at school but they spent so much time getting to school, they were too tired to learn, says their mother, Julia”. ‘We had a family conference and in the end we decided to try homeschooling. So far, it’s been a big success, but the girls know that if they want to go back to school at any time, we’ll let them. We follow the normal school program of lessons, and they will take all the normal school exams.’
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Which of the following is TRUE according to the passage?
Dùng thông tin sau cho Câu 39 và Câu 40: Xét phản ứng tổng hợp hạt nhân:
\(_1^2{\rm{D}} + _1^3\;{\rm{T}} \to _2^4{\rm{He}} + _0^1{\rm{n}}\)
Cho biết khối lượng của các nguyên tử \(_1^2{\rm{D}},_1^3\;{\rm{T}},_2^4{\rm{He}}\) và khối lượng hạt neutron lần lượt là: \(2,0141{\rm{u}};3,0160{\rm{u}};4,0026{\rm{u}};1,0087{\rm{u}}.\)
Năng lượng toả ra khi tổng hợp được \(1,00\;{\rm{mol}}_2^4{\rm{He}}\) từ phản ứng trên có thể thắp sáng một bóng đèn \(100,0\;{\rm{W}}\) trong bao nhiêu năm? (Kết quả làm tròn theo đơn vị năm).Cùng là đường đôi, nhưng đường maltose khác sacrose ở điểm nào dựa vào hình ảnh minh hoạ dưới đây:
Read the following passage and mark the letter A, B, C, or D on your answer sheet to indicate the correct answer.
Global Issues: Gender Equality and Women’s Empowerment
Gender equality means that men and women have equal power and equal opportunities for financial independence, education, and personal development. Women's empowerment is a critical aspect of achieving gender equality. It includes increasing a woman's sense of self-worth, her decision-making power, her access to opportunities and resources, her power and control over her own life inside and outside the home, and her ability to effect change. Yet gender issues are not focused on women alone, but on the relationship between men and women in society. The actions and attitudes of men and boys play an essential role in achieving gender equality.
Education is a key area of focus. Although the world is making progress in achieving gender parity in education, girls still make up a higher percentage of out-of-school children than boys. Approximately one quarter of girls in the developing world do not attend school. Typically, families with limited means who cannot afford costs such as school fees, uniforms, and supplies for all of their children will prioritize education for their sons. Families may also rely on girls' labor for household chores, carrying water, and childcare, leaving limited time for schooling. But prioritizing girls' education provides perhaps the single highest return on investment in the developing world. An educated girl is more likely to postpone marriage, raise a smaller family, have healthier children, and send her own children to school. She has more opportunities to earn an income and to participate in political processes, and she is less likely to become infected with HIV.
Women's health and safety is another important area. HIV/AIDS is becoming an increasingly impactful issue for women. This can be related to women having fewer opportunities for health education, unequal power in sexual partnership, or as a result of gender-based violence. Maternal health is also an issue of specific concern. In many countries, women have limited access to prenatal and infant care, and are more likely to experience complications during pregnancy and childbirth. This is a critical concern in countries where girls marry and have children before they are ready; often well before the age of 18. Quality maternal health care can provide an important entry point for information and services that empower mothers as informed decision-makers concerning their own health and the health of their children.
A final area of focus in attaining gender equality is women's economic and political empowerment. Though women comprise more than 50% of the world's population, they only own 1% of the world's wealth. Throughout the world, women and girls perform long hours of unpaid domestic work. In some places, women still lack rights to own land or to inherit property, obtain access to credit, earn income, or to move up in their workplace, free from job discrimination. At all levels, including at home and in the public arena, women are widely underrepresented as decision-makers. In legislatures around the world, women are outnumbered 4 to 1, yet women's political participation is crucial for achieving gender equality and genuine democracy.
What is the tone of the author in the passage?
Phương pháp nào không phải là phương pháp do kháng sinh có chức năng?