Question

Demographers typically like to know how fast a population is growing at a particular instant in time. Taking the population of the Democratic Republic of the Congo in mid-2008 (N = 67 million) and your estimate of r for this same population (from question 47), use the differential form of the exponential growth model (dN/dt = rN) to estimate the instantaneous rate of population growth in mid-2008, to the nearest tenth of a million persons per year:

A) 0.7
B) 1.0
C) 2.0
D) 3.0

Answer 1

The instantaneous rate of population growth for the Democratic Republic of the Congo in mid-2008 is approximately 0.7 million persons per year when the population was 67 million and the assumed growth rate is 1%.

Step-by-step explanation:

To calculate the instantaneous rate of population growth using the exponential growth model (dN/dt = rN), we need to know the current population size N and the population growth rate r. In mid-2008, the population of the Democratic Republic of the Congo (DRC) was given as 67 million people (N = 67,000,000). The population growth rate (r) given from a previous question, which we assume here could be 1%, and is expressed as a decimal (r = 0.01). The formula then becomes:

dN/dt = rN = 0.01 × 67,000,000

The calculation yields:

dN/dt = 670,000 persons/year

So, to the nearest tenth of a million persons per year, the instantaneous rate of population growth of the DRC in mid-2008 was approximately 0.7 million persons per year, which corresponds to option A.