Question

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 3.11.

Answer 1

Chessville : 50000(1.07)^n
Checkervill: 70000(.96)^n

when is 50000(1.07)^n = 70000(.96)6n
5(1.07)^n = 7(.96)^n
log both sides and use rules of logs

log5 + nlog1.07) = log7 + nlog.96
nlog1.07 - nlog.96 = log7 - log5
n(log1.07 -log.96) = log7 - log5
n = ( log7 - log5)/(log1.07 -log.96)
= 3.101
in about 3 years from 2010 or in the year 2013

check:
50000(1.07)^3 = appr 61252
70000(.96)^3 = 61931
seems plausable, had I used the decimals it would be closer

Answer 2

Thanks!