Final answer:
To determine the doubling time for the population of Abnarca, we first calculate the annual growth rate using the given population sizes for 1980 and 1990. Then, using the exponential growth formula, we solve for the time it would take for the population to double from its original size in 1980.
Step-by-step explanation:
The question at hand involves the exponential growth of populations in two cities, Abnarca and Bonipto. To calculate how long it takes for Abnarca's population to double, we need to use the information given about its population in 1980 and in 1990.
Abnarca's population grew from 25,000 in 1980 to 29,000 in 1990. This represents a growth of 4,000 over 10 years. We can assume exponential growth and use the formula for exponential growth:
P(t) = P₀ * e(rt),
where P(t) is the population at time t, P₀ is the initial population, r is the growth rate, and t is the time period. Since we want to know the doubling time, we set P(t) to be twice P₀.
In this case, P(t) = 2 * 25,000 = 50,000 and P₀ = 25,000. We also know that in 10 years, the population reached 29,000. First, we must find the annual growth rate r using 10 years growth:
29,000 = 25,000 * e(10r),
Solving for r:
r ≈ ln(29,000/25,000) / 10 ≈ 0.01504.
Now we can set P(t) to 50,000 and solve for t:
50,000 = 25,000 * e(0.01504t),
Solving for t gives us:
t ≈ ln(2) / 0.01504 ≈ 46.20.
Therefore, the population of Abnarca takes approximately 46 years to double.