UPSC Prelims 2021 · CSAT
Question 8: Basic Numeracy
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 ?
AnswerUPSC’s answer is (d).
Doubling every 12 years means the population is multiplied by 2 once for each 12-year block. After n years there are n/12 blocks, so P = 50 × 2^(n/12). Check: at n = 12 this gives 100, double the starting 50, and at n = 0 it gives 50. The linear options add a fixed amount each year, which is not doubling, and the 2^(12n) option multiplies by 4096 every year. Remember: growth by a fixed factor over a fixed period is exponential, with the period in the denominator of the exponent.
Why each option is right or wrong
- (a) Adds 50 a year to a starting value of 12; this is linear and starts at the wrong number.
- (b) Adds 12 animals a year: linear, not doubling, though it does start at 50.
- (c) Multiplies by 2^12 = 4096 each year, far faster than doubling every 12 years.
- (d) Right: n/12 counts the 12-year periods, so n = 12 gives 100.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2021, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.