Q. 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)
Correct Answer: (d) P = 50 (2)^(n/12)
Question from UPSC Prelims 2021 CSAT Paper
Explanation :
Biology Class at High School Population Growth Model
Given:
– Initial population (2021) = 50 animals
– Population doubles every 12 years
– Need formula for population P after n years
Step 1: Identify Growth Type
– Not linear growth (population doesn’t increase by fixed amount)
– Population multiplies by 2 at fixed intervals
– This indicates exponential growth
Step 2: Basic Exponential Growth Formula
P = Initial Value × (growth factor)^(time/interval)
Step 3: Identify Components
– Initial Value = 50
– Growth factor = 2 (doubles)
– Time = n years
– Interval = 12 years
Step 4: Analyze Options
a) P = 12 + 50n
Incorrect: Shows linear growth
b) P = 50 + 12n
Incorrect: Shows linear growth
c) P = 50(2)^12n
Incorrect: Time interval ratio is wrong
d) P = 50(2)^(n/12)
Correct: Shows proper exponential growth
Step 5: Verify Option D
After 0 years: P = 50(2)^0 = 50 (correct initial population)
After 12 years: P = 50(2)^1 = 100 (population doubles)
After 24 years: P = 50(2)^2 = 200 (doubles again)
Answer: The correct formula is P = 50(2)^(n/12)
This formula accurately represents population doubling every 12 years from an initial value of 50 animals.
