The world population was 2,560 million in 1950 and 3,040 million in 1960. Assume the growth rate of the population is proportional to the size of the population P (t). Also assume that t = 0 in 1950. When is the world population predicted to reach 10 billion?

The world population will reach 10 billion in approximately 70 years.

That would be in the year 2020

Step-by-step explanation:

The growth rate of the population is in geometric progression.

The formula for the nth term of an arithmetic progression is

ar^ (n-1)

Where a is the first term of the sequence.

r = the common ratio (ratio of a term to the previous term)

n = number of terms.

From the information given

n = t = number of years.

a = 2560000000

T1 = 2560000000r^0 = 2560000000

In 1960, the population is 3040000000.

Number of terms = 11 (1950 to 1960)

T11 = 3040000000 = 2560000000r^10

r^10 = 3040000000/2560000000

r^10 = 1.1875

Taking 10th root of both sides,

r = 1.01733353775

r = 1.02

When the world population becomes 1 billion, the number of years will be

1000000000 = 2560000000 * 1.02^ (n-1)

1.02^ (n-1) = 1000000000/2560000000 = 3.90625

1.02^ (n-1) = 3.90625

1.02^n / 1.02^1 = 3.90625

1.02^n = 1.02 * 3.90625 = 3.984375

1.02^n = 3.99

n = 70

It will reach 10 billion in (1950 + 70) = 2020