Let's solve the given problem step-by-step.
1. Identify Initial Population: The initial population of the rural municipality is given as 28,500.
2. Understand Growth Rate: The population growth rate is 2% per annum (p.a.). In decimal form, this is 0.02 (2% = 2/100 = 0.02).
3. Time Period: The duration over which the population grows is given as 2 years.
4. Calculate Final Population: To find the final population after 2 years, we use the formula for exponential growth:
[tex]\(P_{\text{final}} = P_{\text{initial}} \times (1 + r)^t\)[/tex]
where [tex]\(P_{\text{initial}}\)[/tex] is the initial population, [tex]\(r\)[/tex] is the growth rate, and [tex]\(t\)[/tex] is the time in years.
5. Plug in the Values: Let's plug in the values into the formula.
[tex]\(P_{\text{final}} = 28,500 \times (1 + 0.02)^2\)[/tex]
Now, let's calculate the final population:
[tex]\(P_{\text{final}} = 28,500 \times (1.02)^2\)[/tex]
[tex]\(P_{\text{final}} = 28,500 \times 1.0404\)[/tex] (here, we have calculated [tex]\(1.02 \times 1.02\)[/tex])
[tex]\(P_{\text{final}} = 28,500 \times 1.0404\)[/tex]
[tex]\(P_{\text{final}} = 29,651.4\)[/tex]
6. Calculate Population Increase: To find the increase in population, subtract the initial population from the final population.
Population Increase [tex]\(= P_{\text{final}} - P_{\text{initial}}\)[/tex]
[tex]\(= 29,651.4 - 28,500\)[/tex]
[tex]\(= 1,151.4\)[/tex]
7. Final Answer: Since we can't have a fraction of a person, we'll round this number to the nearest whole number. The population has therefore increased by approximately 1,151 individuals over 2 years.
