I need help please!!!
On January 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 had a population of 70,000 people. Checkersville starts to experience a population decline. Its population decreases 4% each year. During what year will the population of Chessville first exceed that a Checkersville? Show all of your work and explain your steps.
Any help would be great.
50000 + 0.07x*50000>70000-0.04x*70000.
50000 + 3500x > 70000 - 2800x
3500x + 2800x > 70000 - 50000
6300x > 20000
X > 3.17 yr.
So the population of Chessville becomes greater than the population of Checkers-
ville during the 3rd yr.
Correction: Change > to =.
X = 3.17460 Years.
To determine the year when the population of Chessville first exceeds that of Checkersville, we need to calculate the population of both towns for each year until that happens.
First, let's find the population for each town in the year 2011. For Chessville, we need to increase the initial population of 50,000 by 7%:
Population of Chessville in 2011 = 50,000 + (7/100) * 50,000 = 50,000 + 3,500 = 53,500
For Checkersville, we need to decrease the initial population of 70,000 by 4%:
Population of Checkersville in 2011 = 70,000 - (4/100) * 70,000 = 70,000 - 2,800 = 67,200
Next, we will repeat the process for each subsequent year until the population of Chessville exceeds that of Checkersville.
In 2012, the population of Chessville will be:
Population of Chessville in 2012 = Population in 2011 + (7/100) * Population in 2011 = 53,500 + (7/100) * 53,500 = 53,500 + 3,745 = 57,245
In 2012, the population of Checkersville will be:
Population of Checkersville in 2012 = Population in 2011 - (4/100) * Population in 2011 = 67,200 - (4/100) * 67,200 = 67,200 - 2,688 = 64,512
We continue this process until the population of Chessville exceeds that of Checkersville.
Now, you can continue the above calculations for each subsequent year by applying the same formulas:
In 2013:
Population of Chessville = Population in 2012 + (7/100) * Population in 2012
Population of Checkersville = Population in 2012 - (4/100) * Population in 2012
Repeat this process for each year until the population of Chessville first exceeds the population of Checkersville. You might find it helpful to use a spreadsheet or a calculator to calculate the population values for each year.
Continue this process until the population of Chessville first exceeds the population of Checkersville. Keep track of the year and population values for each town.
Once you find the year when the population of Chessville exceeds that of Checkersville, you will have your answer.
Note: I have provided the general steps to solve this problem. You will need to perform the calculations for each year to find the exact year when the population of Chessville first exceeds that of Checkersville.