40000(1.03)^x=84000(.98)^x

Question

Pacetown had a population of 40000 and its population is steadily growing at 3% per year. Gerrytown has a population of 84000 and steadily decreasing at the rate of 2% per year. How many years will they have the same population?

Answer 1

40,000*(1.03)^x = 84,000*(0.98)^x

1.03^x=2.1*(0.98)^x

take log10 av both sides...x*log(1.03)=log(2.1)+x*log(0.98)

0.012837224705172283 x=0.32221929473392097 -0.008773924307505197x1929
0.0216114901267748x=0.32221929473392097

x=0.322219... / 0.02161149...

=14.909864104584212 yeers

or bout 15 yeers