assuming the growth is exponential, when would the population of austin and columbus be equal.(look in detail)

Question

using the data in the table below and assuming the growth is exponential, when would the populations of Austin and Columbus be equal?

Austin: population: 1990=465,622 2000=656,562
Columbus: population: 1990= 632,910 2000=711,265

Answer 1

656,562 = 465,622 e^10k
656,562/465,622 = e^10k
ln(656,562/465,622) = 10k
k = 0.1*ln(656,562/465,622) = .034
So for Austin we have P =465,622e^.034t

Similarly for Columbus we have:
P = 632910 e^ .0117t

Populations will be same when:
465622e^.034t = 632910 e^.012t
e^.022t = 632910/465622 = 1.36
t = ln(1.36)/.022 = 14 years
which would be at end of 2004