The population of towns A and B increase at the rate proportional to their population present at that time. At the end of the year 1984, the population of both the towns was 20,000 . At the end of the year 1989, the population of town A was 25,000 and that of town B was 28,000. The difference of populations of towns A and B at the end of 1994 was

Step-by-step solution

The population growth of both towns follows the exponential model P(t) = P₀ e^ kt , with initial population P₀ = 20, !000 at t=0 (end of 1984). For town A, the population at t=5 (end of 1989) is 25, !000 , giving e^ 5k_A = 25, !000 / 20, !000 = 1.25 . The population at t=10 (end of 1994) is therefore P_A(10) = 20, !000 (1.25)^2 = 31, !250 . For town B, the population at t=5 is 28, !000 , yielding e^ 5k_B = 28, !000 / 20, !000 = 1.4 . The population at t=10 is P_B(10) = 20, !000 (1.4)^2 = 39, !200 . The difference i