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 Population Growth Model
The biology class predicted that the population of animals will double in size every 12 years. This means that the population follows an exponential growth model. The general form of an exponential growth model is P = P0 * (1 + r)^t where P0 is the initial population, r is the growth rate, and t is time.
In this case, since the population doubles every 12 years, we can write the equation as P = P0 * 2^(t/12) where t is measured in years.
Since the initial population at the beginning of 2021 was estimated to be 50 animals, we can substitute P0 = 50 into the equation to get: P = 50 * 2^(n/12).
Best Method – Check All Options
