What you must do is evaluate the function for the given conditions and thus be able to find the constants A and k
25 = Ae ^ k (2005)
31 = Ae ^ k2010
We then have two equations with two unknowns.
Solving.
25/31 = e ^ k (2005-2010)
Ln (25/31) = k (2005-2010)
k = Ln (25/31) / (2005-2010) = 0.043
Substituting k in any of the equations:
25 = Ae ^ (0.043 * (2005))
Clearing A
A = 25 / (e ^ (0.043 * (2005))) = 9.02E-37
Then, by 2020
P = (9.02E-37) e ^ (0.043 * (2020)) = 48 million
answer
the population for 2020 will be 48 million