Exponential functions - which is the better solution?

jeudi 1 août 2013

1. The problem statement, all variables and given/known data

A town's population grows at 6.5% per annum. How many are in town now, if there will be 15 000 in 4.5 years?

Please explain which of these solutions is best. Or explain a better solution, please.

2. Relevant equations

A(t) = Pe^r(t) <- general approach

A = P(1+i)^t <- compound interest formula (is this too simplified?)

In both cases, A is the number of people at time, t. P is the current population (solving for P). The rate is r, or i. & e is Euler's number.

3. The attempt at a solution

Solution 1.

A(t) = Pe^r(t)

15000 = Pe^(0.065)(4.5)

P = (15000)/(e^(0.065)(4.5))

P = 11 195.9287

Solution 2.

A = P(1+i)^t

15000 = P(1.065)^4.5

P = 15000/(1.065^4.5)

P = 11 298.4280

Why the difference? Which solution is better? Is the compound interest formula an over-simplification?

Many thanks!