Answers to Population Problems


PROBLEMS
  1. There are already places on earth where population densities approach the 1 person/m2 . A two story building in Delhi, india was found to house 518 individuals (density of 1 person/ 1.5 m2). Calculate the floor area of the building in Delhi. Compare this to the average floor area of the typical single family home built in the U.S. in 1995 (2095 ft2).

    The density of the building housing 518 people is 1 person per 1.5 m2.
    The floor area is most easily determined using a proportionality:

    1 person = 518 people
    1.5 m2            x


    Crossmultiplying yields:

    (x)(1 person) = (1.5 m2(518 people)
    x = (518 people)(1.5 m2)
            (1 person)
    x = 777 m2


    If the average floor area of a new single family dwelling in the U.S. was 2095 ft2. To compare this to the floor area of the Delhi dwelling, you must convert one of the figures so that both numbers are in the same unit of measure, either square feet or square meters.

    777m2 x (3.281 ft)2/m2 = 8364 ft2
    8364 ft2/2095 ft2 = 4.0


    Incredibly, the Delhi building is only 4 times larger than a typical American home built in 1995, yet it housed more than 500 people!


  2. The land area of Brooklyn, NY is 70.5 mi2 (1990 data). In 1992 the population of Brooklyn was 2,286 million. Calculate the population density of Brooklyn in terms of people per square meter.
    (1 mi2 = 2.6 km2 )

    First convert square miles to square meters:

    70.5 m2 x (1609 m)2/(mi)2 = 1.825 x 108 m 2

    Next determine the population density:

    2,286,000 people/(1.825 x 108 m 2) = 0.0125 people/m2

    or 1.25 x 10-2 people/m2


  3. If the earth's population growth is 1.36% per year, in what year will the world population reach the same density as Brooklyn's 1992 population density? Is it likely that this density will ever be reached?

First determine how many people there would be on the planet at the density of Brooklyn; calculate as follows:

(1.25 x 10-2 people/ m2 x (1.24 x 10 14 m2 of dry land) = 1.55 x 1012 people

Using the formula t = (1/k)ln(N/N0), solve for t:

t = (1/0.0136)ln[(1.55 x 1012)/(5.85 x 109)] = 410 yrs

1997 + 410 = 2407