Question

The population of a city increases in size by 18 percent every 12 years.

By what percentage will the population have increased after 27 years? (Give your answer correct to at least two decimal places.)

_____%

By what percentage does the growth rate of the city increase over a 12 year period? (Give your answer correct to at least two decimal places.)

_____%

At what rate would the be population growing when there are two hundred thousand people living in the city? (Give your answer correct to the nearest integer.)

_____ people per year.

At what rate will the population be growing 2 years later? (Give your answer correct to the nearest integer.)

_____ people per year.

Answer 1

From this given scenario in the problem, the population after n years is equal to,
                                   P(n) = P(1 + r)^(n/12)

a. After 27 years,
                                    P(n) = P(1 + 0.18)^(27/12) = 1.45P
Therefore, after 27 years, the population will grow by 45.12%

b. After 12 years, it is given that the population will increase by 18%

c. If there are 200,000 people living in the city, the population after a year will be,
                           rate of change = (200,000)(1.18)^(1/12) - 200,000 = 2778

d. After 2 years,
                          rate of change = (200000)(1.18)^(2/12) - 200000 = 5594