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?

Answer:The world population will reach 10 billion in approximately 70 years.That would be in the year 2020Step-by-step explanation:The growth rate of the population is in geometric progression.The formula for the nth term of an arithmetic progression isar^(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 givenn = t = number of years.a = 2560000000T1 = 2560000000r^0 = 2560000000In 1960, the population is 3040000000. Number of terms = 11 (1950 to 1960)T11 = 3040000000= 2560000000r^10r^10 = 3040000000/2560000000 r^10 = 1.1875Taking 10th root of both sides, r = 1.01733353775r = 1.02When the world population becomes 1 billion, the number of years will be1000000000= 2560000000 × 1.02^(n-1)1.02^(n-1) = 1000000000/2560000000 = 3.906251.02^(n-1) = 3.906251.02^n / 1.02^1 = 3.906251.02^n = 1.02 × 3.90625 = 3.9843751.02^n = 3.99n = 70It will reach 10 billion in (1950 + 70 )= 2020