On Jan 1, 2010, Chessville has a population of 50,000 people. Chessville then enters a period of population growth. Its population increases 7% each year. On the same day, Checkersville has a population of 70,000 people. Checkersville starts to experience a population decline. its population decrease 4% each year. During what year will the population Chessville first exceed that of Checkersville? Show work and explain steps.
My answer is 3.16. Is this correct?
Actually my answer is 3.11.
To find out the year when the population of Chessville first exceeds that of Checkersville, we need to perform some calculations based on the given data.
Let's assume that the current year is 2010 and we'll track the population growth over the years until Chessville's population exceeds Checkersville's population.
First, we'll calculate the population of each town for subsequent years and compare them until Chessville's population overtakes Checkersville's.
Here are the steps to determine the answer:
1. Calculate the population of Chessville and Checkersville for each year until Chessville's population exceeds Checkersville's.
Start with the given population figures:
Chessville (Jan 1, 2010): 50,000
Checkersville (Jan 1, 2010): 70,000
2. For each subsequent year after 2010, use the population growth rates to calculate the new populations of both towns.
For Chessville, the population increases by 7% each year, so we can calculate the population for each year using the formula:
Population of Chessville (after n years) = Population of Chessville (Jan 1, 2010) × (1 + growth rate)^n
For Checkersville, the population decreases by 4% each year, so we can calculate the population for each year using the formula:
Population of Checkersville (after n years) = Population of Checkersville (Jan 1, 2010) × (1 - decline rate)^n
3. Keep calculating and comparing the populations until Chessville's population exceeds Checkersville's.
Let's do the calculations:
Year 2010:
Chessville population = 50,000
Checkersville population = 70,000
Year 2011:
Chessville population = 50,000 × (1 + 0.07)^1 ≈ 53,500
Checkersville population = 70,000 × (1 - 0.04)^1 ≈ 67,200
Year 2012:
Chessville population = 50,000 × (1 + 0.07)^2 ≈ 57,045
Checkersville population = 70,000 × (1 - 0.04)^2 ≈ 64,512
Continue this process until Chessville's population exceeds Checkersville's population.
4. The year when Chessville's population first exceeds Checkersville's population is the answer.
Based on the calculations, the population of Chessville exceeds Checkersville in the year 2016. Therefore, the correct answer is not 3.16 but 2016.
In summary, to find the year when Chessville's population exceeds that of Checkersville, we need to calculate the population growth of both towns for each year and compare them until Chessville overtakes Checkersville.