Question

The population of a country has a relative growth rate of 2% per year. The government is trying to reduce the growth rate to 1%. The population in 2011 was approximately 150 million. Find the projected population (in million people) for the year 2039 for the following conditions. (Round your answers to the nearest million.)

(a) The relative growth rate remains at 2% per year.

(b) The relative growth rate is reduced to 1% per year.

Answer 1

To find the projected population for the year 2039 under different growth rate conditions, we can use the formula for exponential growth:

P = P0 * (1 + r)^t

Where:

P is the projected population in the future

P0 is the initial population (in 2011, approximately 150 million)

r is the relative growth rate (expressed as a decimal)

t is the number of years into the future

(a) The relative growth rate remains at 2% per year:

Using r = 0.02 and t = 2039 - 2011 = 28 years:

P = 150 million * (1 + 0.02)^28

P ≈ 150 million * (1.02)^28

P ≈ 150 million * 1.6653

P ≈ 249.8 million

The projected population for the year 2039, assuming a 2% growth rate, is approximately 250 million.

(b) The relative growth rate is reduced to 1% per year:

Using r = 0.01 and t = 2039 - 2011 = 28 years:

P = 150 million * (1 + 0.01)^28

P ≈ 150 million * (1.01)^28

P ≈ 150 million * 1.3174

P ≈ 197.6 million

The projected population for the year 2039, assuming a 1% growth rate, is approximately 198 million.

Please note that these calculations are based on the assumption of continuous exponential growth and do not take into account other factors that may affect population growth.