Question

In 2010, a city's population was 1,405,233 and it was decreasing at a rate of 1.1%. At this rate when will the city's population fall below 1,200,000?
a. 2024
b. 2027
c. 2036
d. 2049

Answer 1

The equation
                                            P(t) = 1405233 * (1 - 0.011)^(t)
models the population at t years after 2010. Then, when P(t) = 1,200,000, we have
                                 1200000 = 1405233 * (0.989)^t
                                  (0.989)^t = 1200000/1405233
                                                t = log(1200000/1405233)/log(0.989)
                                                t = 14.27 years
This means 14.27 years after 2010. Therefore, the answer to this question is 2024.