Question

The town of Pawnee, Indiana has a population of 65,000 and is growing at a rate of 1800 people a year. The neighboring city of Eagleton, Indiana has a population of 81, 500 and is decreasing at a rate of 560 people a year. After how many years will Pawnee's population be the same as Eagleton's population?

Answer 1

Answer: 7 years

Step-by-step explanation: To find out after how many years Pawnee's population will be the same as Eagleton's population, we need to determine the difference in population between the two towns and divide it by the difference in growth rates.

Let's calculate the difference in population between Pawnee and Eagleton:

Pawnee's population: 65,000

Eagleton's population: 81,500

The difference in population is: 81,500 - 65,000 = 16,500

Now, let's calculate the difference in growth rates between the two towns:

Pawnee's growth rate: 1800 people/year

Eagleton's growth rate: -560 people/year (negative because it's decreasing)

The difference in growth rates is: 1800 - (-560) = 1800 + 560 = 2360

To find out how many years it will take for Pawnee's population to be the same as Eagleton's population, we need to divide the difference in population by the difference in growth rates:

Years = Difference in population / Difference in growth rates

Years = 16,500 / 2360

Calculating this division, we find that it will take approximately 7 years for Pawnee's population to be the same as Eagleton's population.