Final answer:
It will take 15 years for the population to reach 24,600. To find out how long it will take for the town's population to reach 24,600, we can use the formula for exponential growth and solve for the time in years.
Step-by-step explanation:
In order to project the time required for the town's population to reach 24,600, the formula for exponential growth is applied: P = P0 * (1 + r)^t.
Here, P represents the future population, P0 is the initial population, r denotes the growth rate, and t signifies time in years.
Substituting the provided values, the equation becomes 14,000 * (1 + 0.045)^t = 24,600.
Simplifying further yields (1.045)^t = 24,600 / 14,000.
Taking the logarithm of both sides and solving for t results in the formula t = log(24,600 / 14,000) / log(1.045).
Utilizing a calculator, the calculated value is approximately 15.34 years.
Rounding to the nearest year, the prediction suggests that it will take 15 years for the population to reach 24,600, reflecting the application of exponential growth principles in demographic forecasting.