Question

The population in Kingstown decreases by 30% each month. By what percent did the original population decrease after 2 months? A. 40% B. 49% C. 51% D. 60%

Answer 1

C. 51%

Explanation:

Let P represent the original population.

Given that the population decreases by 30% monthly

After one month P would have decreased

P - 30%P = P(1 - 0.3)

The population at time t months can be written as;

P(t) = P(1 - 0.3)^t

P(t) = P(0.7)^t

For t = 2 months

P(2) = P(0.7)^2

P(2) = P(0.49)

P(2) = 49% of P

Therefore, the population have decreased by

∆P = P - P(2) = P - 49% of P = P(100% - 49%)

∆P = 51% of P

The population have decreased 51%