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subject to $ x, y > 0 $. - SUpost

📅 July 5, 2026 👤 scraface

Jul 05, 2026

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📌 A philosopher of science tracks paradigm shifts: every 25 years, a new framework explains 30% more phenomena than the previous. Starting from 100 explained units, how many are explained after 75 years?

📌 A science journalist models viral science videos: a video gains 150% more views each day. If it starts with 1,000 views on Day 0, how many views does it have at the end of Day 3?

📌 A pharmacologist develops a treatment that clears a toxic protein at a rate of 20% per day. If a brain region initially contains 1,500 mg of the protein, how much remains after 5 days?

📌 A philosopher of science compares two theories: Theory A gains acceptance at 7% annually, starting with 40% public support, while Theory B grows at 10% annually from 25%. After 5 years, which has higher acceptance, and by how many percent points?

📌 Okay, lets tackle this query. The user wants me to generate Algebra questions similar to the provided fragments but not exact copies. They also want the questions inspired by three different personas: a computer scientist at Stanford, a meteorologist, and a science historian. Each question should be a single line with a detailed solution in LaTeX, ending with the boxed answer.

📌 First, I need to understand the original fragments. They include finding the largest x, sequences of numbers, expanding products, functions evaluated at a point with a parameter m, and an equation involving x. The difficulty seems moderate, suitable for a math olympiad.

📌 Now, the personas. Lets brainstorm ideas for each:

📌 Let me start with the computer scientist. A sequence defined by a recurrence relation. For example, a sequence where each term is a function of the previous, and finding a maximum term. Or maybe a problem involving binary trees or bitwise operations, but since its algebra, perhaps a recurrence.

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