The population of the world was approximately 63 billion In

The population of the world was approximately 6.3 billion In July 2003. Assuming that the population will grow by 2 percentage In 1 year, estimate the following. (Round your answers to one decimal place.) How long will It take for the population of the world to double? How long will It take for the population of the world to triple?

Solution

(a) Consider A = P(1+r)^t

Now P is initial population = 6.3

A = amount after t years = double of initial = 2(6.3) = 12.6

r = rate of increase =0.02

So we get , 12.6 = 6.3(1.02)^t

=> 2 = (1.02)^t

=> ln(2) = t ln(1.02)

=> 0.69315/0.01980 = t

=> t = 35.0 years

(b) Now for triple, A = 3(6.3) = 18.9

Hence we get 18.9 = 6.3(1.02)^t

=> 18.9/6.3 = (1.02)^t

=> 3 = (1.02)^t

=> ln(3) = t ln(1.02)

=> 1.0986 = 0.01980 t

=> t =- 55.5 years