a. To project the population of each nation in the year 2010, we can use the formula for exponential growth:
Population = Initial Population * (1 + Growth Rate)^(Number of Years)
For Chad:
Initial Population = 5.2 million
Growth Rate = 2.5% per year
Number of Years = 2010 - 1992 = 18 years
Population of Chad in 2010 = 5.2 million * (1 + 0.025)^(18)
= 5.2 million * (1.025)^18
≈ 5.2 million * 1.5099804664498366
≈ 7.865 million
For Denmark:
Initial Population = 5.2 million
Growth Rate = 0.1% per year
Number of Years = 2010 - 1992 = 18 years
Population of Denmark in 2010 = 5.2 million * (1 + 0.001)^(18)
= 5.2 million * (1.001)^18
≈ 5.2 million * 1.018188532121686
≈ 5.302 million
Therefore, the projected population of Chad in 2010 would be approximately 7.865 million, while the population of Denmark would be approximately 5.302 million.
b. To determine when the population of Chad reaches 10 million, we can set up the exponential growth formula and solve for the number of years:
10 million = 5.2 million * (1 + 0.025)^t
Dividing both sides of the equation by 5.2 million and taking the natural logarithm (ln) of both sides, we get:
ln(10/5.2) = t * ln(1.025)
Simplifying further, we find:
t = ln(10/5.2) / ln(1.025)
≈ 16.4 years
Therefore, the population of Chad is estimated to reach 10 million approximately 16.4 years from 1992, which would be around the year 2008.
To determine the population of Denmark at this time (2008), we can use the exponential growth formula:
Population of Denmark in 2008 = 5.2 million * (1 + 0.001)^(2008 - 1992)
= 5.2 million * (1.001)^16
≈ 5.2 million * 1.01653286
≈ 5.301 million
Therefore, the population of Denmark at the time Chad's population reaches 10 million (around 2008) would be approximately 5.301 million.