Use the approximate doubling time formula rule of 70 in the

Use the approximate doubling time formula (rule of 70) in the question. A city\'s population is growing at a rate of 2% per year. What is its doubling time? By what factor will the population increase in 50 years?

Solution

A = P(1+ r) ^t   where A= future value , P = present avalue , r= 2/100 = 0.02 , t= time

A =2P

So

2P = P(1+0.02)^t

=> 2 =(1.02)^t

=> ln 2 = t ln(1.02)

=> t= ln 2/ ln 1.02 = 35 years (approx)

When t = 50,

A =P (1+ 0.02)⁵⁰

=> A/ P = (1.02)⁵⁰ = 2.69

So Population will get increased by 2.69 times