Final answer:
The question involves calculating population projections using exponential growth. If a town's population doubles every 10 years, we validate the population of 100 reaching 102,400 in 100 years and use the doubling rate to project populations at future time points.
Step-by-step explanation:
The question is related to the population projection of a town based on a mathematical function of growth. If we assume that a town's population doubles every 10 years (which corresponds to a 7% growth rate), we can use exponential growth to predict the population at different points in time.
1. To verify the population of a town of 100 residents in 1900 reaching approximately 100,000 in the year 2000 with a doubling time of 10 years, we would calculate the number of doublings from 1900 to 2000, which is 10. Since 210 = 1024, and the initial population was 100, the population would be 100 * 1024, which equals 102,400.
2. In terms of reaching a population similar to the world's current population, we utilize the same doubling method. It takes 260 years (or 26 doublings) for the population to reach this size. So, we calculate 226 times the initial population of 100, which would give us over 7 billion, verifying the text's claim.
3. To predict the population of the town in future years, we would calculate the number of doublings that will occur in those years and multiply the result by the initial population.