Now I want to know what the actual answer is.
trx123 wrote:
I think 2015 is the right answer. But what's wrong with this?
An exponential function can be used to model population growth that has a constant percentage change in population:
\(f(t)=ab^t\)
Where
f(t)= population after t years
a=initial value
b=growth factor
t=time in years
For town A:
\(9040=10000b^8\)
\(b=(9040/10000)^{1/8}=.987\)
For town B:
\(4560=4000b^4\)
\(b=(4560/4000)^{1/4}=1.033\)
Equating the two functions with an initial value corresponding to the year 1998 we get:
\(9040(0.987)^t=4560(1.033)^t\)
\(t=log1.98/(log1.033-log0.987)=14.99\)
Therefore, 15 years after 1998, or in 2013, the populations of towns A and B will be the same.
Your approach is different from mine in that I used constant numerical rate approach whereas you used a constant percent rate approach.
The two approach has to lead to different answers.
Your approach would show that Town A's population is decreasing at 1.3% per year.
Whereas my approach would show that Town A's population is decreasing at 120pp/year.
The thing to note about percent rate of change is that the number of population change would either accelerate or decelerate as time goes on.
Therefore, since Town A's population is decreasing, the number of population decreasing would gradually become smaller, whereas the number of population increase in Town B's population would gradually accelerate.
Because of this reason, the crossing point for the two towns would come earlier in the constant percent rate analysis than the crossing point for the two towns in the constant numerical rate analysis.
If I was given this on the GMAT I would just use the numerical rate approach and move on. If I tried to go the percent route, I might stress myself too much and jeopardize the rest of the QUANT section
Anyone else have a take on this?