Population Model

Question

World's population in 1950 was 2,555,982,611 with a growth rate of 1,68\% Find an expression for the population over time. ii) Find the population in 2011 if the growth rate prevails.

iii) When will the population reach 7 billion?

iv) v)

Find the doubling time Plot the expression from part (a)

Answer 1

i) P(t) = P₀(1 + 0.0168)^t; P = 2555982611·1.0168^t, where t is number of years after 1950.

ii) In 2011 t = 2011 - 1950 = 61; P(2011) = 2555982611·1.0168⁶¹ = 7,061,967,114

iii) 7 = 2.555982611·1.0168^t; t = ln(7/2.555982611)/ln1.0168 = 60.471 years; In midle of 1950 + 60 = 2010

P(2010.471) = 7 billions

iv) 2P₀ = P₀·1.0168^t; t = ln2/ln1.0168 = 41.6 years. So in 1950 + 41.6 = 2011.6 population was dabbled