Final answer:
The population will reach 50,000 before 260 years, but the exact year is not provided.
Step-by-step explanation:
The population of the town doubles every 10 years and is projected to reach 7 billion in 260 years. To find out when the population will reach 50,000, we can calculate the number of doubling times it would take to reach that population.
Since the population doubles every 10 years, we divide 260 (the number of years it takes to reach 7 billion) by 10 to find the number of doubling times. 260 divided by 10 is 26, so there are 26 doubling times.
To calculate when the population will reach 50,000, we can multiply the starting population of 100 by 2 raised to the power of 26 (the number of doubling times). Using a calculator, we find that 226 is approximately 67,108,864. Multiplying this by 100 gives us a population of approximately 6,710,886,400. Therefore, the population will reach 50,000 well before 260 years, and the exact year when it will reach 50,000 is not given in the information provided.