The 2000 census recorded a population of 16.1 million in a certain country, while in 2010 the figure was 32.8 million. Assuming that the rate of population growth is proportional to the population, predict the population in the year 2015.
A) 39.8 million
B) 46.8 million
C) 36.8 million
D) 41.8 million
E) 52.8 million

Question

Quizplus · Accepted Answer

This problem can be solved using the formula for exponential growth, $P(t) = P_0e^{rt}$, where $P(t)$ is the population at time $t$, $P_0$ is the initial population, $r$ is the rate of growth, and $t$ is the time in years. Given the population doubles from 16.1 million to 32.8 million in 10 years (2000 to 2010), we can find $r$ and then use it to predict the population in 2015. Solving for $r$ gives us a growth rate that, when applied from 2010 to 2015 (5 years), predicts a population of approximately 46.8 million.

The 2000 Census Recorded a Population of 16