Question

It is estimated by experts on agriculture that one-third of an acre of land is needed to provide food for one person on a continuing basis. It is also estimated that there are 10 billion acres of arable land on earth, and that therefore a maximum population of 30 billion people can be sustained if no other sources of food are known. The total world population at the beginning of 1970 was 3.6 billion. Assuming that the population continues to increase at the rate of 2 percent per year, when will the earth be full? What will be the population in the year 2000?

Answer 1

(a)

In 1970, population = 3.6 billion = 3,600,000,000

Rate of Increase = 2% per year

Earth will be full, when population = 30 billion = 30,000,000,000

So,
P = 3,600,000,000

A = 30,000,000,000

R = 2

The formula is:

                                 (1)

Substituting vlues in (1), we get:

So,

i.e.,

1.02^N = 8.3333

Taking logarithm on both sides, we get:

N 0.0198=2.1203

So,

N = 2.1203/0.0198

= 107.0838

So,

the earth will be full in 1970 + 107 = 2077

(b)

To find the population in 2000:
N = 2000 - 1970 = 30

Substituting in (1), we get:

= 6.52 billion