Question

On January 1, 2010, Chessville has a population of 50,000 people. Chessville then enter 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 decreases 4% each year. During what year will the population of Chessville first exceed that of Checkersville? Explain the steps.

Answer 1

\[P_1=50,000(1+7/100)^n=50,000·1.07^n\]\[P_2=70,000(1-4/100)^n=70,000·0.96^n\]\[P_1>P_2 \rightarrow 50,000·1,07^n>70,000·0.96^n \rightarrow \left( \frac{ 1.07 }{ 0.96} \right)^n=1.115^n>\frac{ 7 }{ 5 }=1.4\]\[1.115^n>1.4 \rightarrow n·Log(1.115)>Log(1.4) \rightarrow n>\frac{ Log(1.4) }{ Log(1.115)}=3.1\]
As n>3.1, that means it will happen during the fourth year

Answer 2

Where P1 is Population of Chessville and P2 is Population of Checkersville
"n" is number of years

Answer 3

Thank you!

Answer 4

you are welcome