How long before the human reaches 14 billion people Given we

How long before the human reaches 14 billion people? Given we\'re growing at 2% (r=0.02). I have an answer of 34 years, but I don\'t know the math formula behind that answer

Solution

Future population = Present population x [(1 + Annual growth rate)^{no of years}]

14 x 10⁹ = 7.347 x 10⁹ x [(1 + 0.02)^{no of years}]

[(1 + 0.02)^{no of years}] = 1.905

(1.02)^{no of years} = 1.905

Let no of years be n.

(1.02)ⁿ = 1.905

Taking natural log on both sides,

ln((1.02)ⁿ )= ln(1.905)

n x ln(1.02)= ln(1.905)

n = ln(1.905) / ln(1.02)

n = 32.54

Answer: It will take 32.54 year before the human reaches 14 billion people.