The population of a country in 2005 was 25 million. in 2010 it was 31 million. estimate the population in 2020. use the formula p=ae^kt

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