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)ⁿᐟ¹² ✓ UPSC's answer
Why the answer is (d)
• Doubling every 12 years means that after n years the population has doubled n/12 times.
• Starting from 50, the population after n years is P = 50 × 2ⁿᐟ¹².
• Check: at n = 12, P = 50 × 2 = 100; at n = 24, P = 50 × 4 = 200.
• Hence P = 50 (2)ⁿᐟ¹², option (d).
Why the other options are wrong
- (a) P = 12 + 50n
- P = 12 + 50n is linear growth of 50 a year, not doubling every 12 years.
- (b) P = 50 + 12n
- P = 50 + 12n is linear growth of 12 a year, not doubling every 12 years.
- (c) P = 50 (2)¹²ⁿ
- P = 50 (2)¹²ⁿ would double 12 times every year, not once every 12 years.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2021, held on 10 October 2021. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.