To answer this question, we need to calculate the population of both towns for each year and compare them.
For Town A:
1980 population = 1200
1981 population = 1200 + 300 = 1500
1982 population = 1500 + 300 = 1800
1983 population = 1800 + 300 = 2100
and so on
For Town B:
1980 population = 500
1981 population = 500 + 0.12(500) = 560
1982 population = 560 + 0.12(560) = 627.2
1983 population = 627.2 + 0.12(627.2) = 702.464
and so on
To determine which town will eventually have the greater population, we can calculate the limit of each population as time goes to infinity. For Town A, the population limit is infinity because the population keeps increasing by 300 every year. For Town B, the population limit is also infinity because the population grows exponentially due to the 12% increase each year. However, we can still compare their growth rates.
For Town A, the annual growth rate is constant at 300 people per year, whereas for Town B, the growth rate is decreasing over time due to the compounding effect of the percentage increase.
Therefore, initially, Town A has a smaller population than Town B. However, over time, Town A's growth rate remains constant while Town B's growth rate slows down. Eventually, Town A will surpass Town B in population.
To determine which town had a greater population in 2005, we need to calculate the population of each town in 2005 using the growth rates we calculated above.
For Town A:
1980 population = 1200
2005 population = 1200 + 300(25) = 8700
For Town B:
1980 population = 500
2005 population = 500(1.12)^25 = 4544.73
Therefore, in 2005, Town A had a greater population than Town B.