Final answer:
The question requires solving for the exponential growth rates of the cities Abnarca and Bonipto and then using those rates to project future population sizes. Abnarca's growth rate is calculated using its known population sizes in 1980 and 1990, while Bonipto's growth rate is calculated based on its population doubling every 55 years.
Step-by-step explanation:
The problem involves exponential population growth of the cities of Abnarca and Bonipto. We can start by calculating the growth rate of Abnarca's population. We know that in 1980, Abnarca had a population of 21,000 people which grew to 26,000 in 1990. This is a 10-year period. The exponential growth rate can be calculated using the formula P = P0 * e^(rt), where P is the final population, P0 is the initial population, r is the growth rate, and t is time in years. Rearranging the formula to solve for r gives us r = (ln(P/P0))/t.
For Abnarca, we have:
- Initial population (P0) = 21,000
- Final population (P) = 26,000
- Time (t) = 10 years
Plugging these into the formula, r = (ln(26,000/21,000))/10.
For Bonipto, we use the doubling time formula Td = ln(2)/r to find the growth rate. Bonipto has a doubling time (Td) of 55 years:
r = ln(2) / 55
Using these growth rates, we can then calculate future population projections for both cities, according to their individual growth models. For example, to calculate the population of Abnarca in a given year, we return to the exponential growth formula and apply the growth rate we calculated for Abnarca to the new time period.
These calculations allow us to provide correct answer by solving for the exponential growth rates and future populations of the cities of Abnarca and Bonipto.