Question

The population of a city was 34,000 at the beginning of 1937. Its

population steadily increased by 6.8% every year from 1937 to 1997.
Which of these is the closest to the population of the city at the end of
1970?

Answer 1

298078.228074

Explanation:

we add 6.8% of the population to the city each year

city population in year x + 1 = city population in year x + 6.8% of city population in year x = city population in year x + 0.068 * city population in year x = 1 * city population in year x + 0.068 * city population in year x = 1.068 * city population in year x

we multiply the population by 1.068 each year to get the next year's population

thus, over a period of y years, we would multiply the population by 1.068 y times.

start = 34000 in 1937

difference in years = 1970 - 1937 = 33

final amount = 34000 * 1.068 33 times = 34000 * 1.068^33 = 298078.228074