एक हाई स्कूल की जीवविज्ञान की कक्षा ने पूर्वानुमान लगाया कि पशुओं की स्थानीय आबादी प्रत्येक 12 वर्ष में दुगुनी हो जाएगी । किए गए आकलन के अनुसार वर्ष 2021 के आरंभ में पशुओं की आबादी 50 होगी । यदि n वर्षों के पश्चात की आबादी को P से निरूपित किया जाता है, तो निम्नलिखित में से कौन-सा समीकरण, कक्षा द्वारा बनाए गए आबादी के मॉडल को निरूपित करता है ?
Read this question in English
A biology class at high school predicted that a local population of animals will double in size every 12 years. The population at the beginning of the year 2021 was estimated to be 50 animals. If P represents the population after n years, then which one of the following equations represents the model of the class for the population?
(a) P = 12 + 50n · (b) P = 50 + 12n · (c) P = 50 (2)^(12n) · (d) P = 50 (2)^(n/12)
उत्तर और व्याख्या · explanation in English
Answer: (d) P = 50 (2)^(n/12)
Doubling every 12 years is exponential growth: after n years the population has doubled n/12 times, so P = 50 × 2^(n/12). Putting n = 0 and n = 12 (giving 50 and 100) confirms it and rules out the other options.
- Doubling every 12 years means multiplying by 2 once for each 12-year block.
- In n years there are n/12 such blocks, so P = 50 × 2^(n/12).
- Check: n = 0 gives 50; n = 12 gives 100; n = 24 gives 200 — doubling every 12 years.
- Options (a) and (b) add a fixed number each year (linear growth); (c) gives 50 × 2¹² at n = 1, far too fast.
Remember · Test formula options by plugging in simple values — the start (n = 0) and one full period.
Question and answer: UPSC's official GS Paper II (2021, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·