Question

if the population of a country increases at a rate of 1.5% annually, and it’s current population is 430,000, how many years will it take for the population to triple

Answer 1

Hi,
$a_0=430000\\ a_1=a_0*1.15\\ a_2=a_1*1.15=a_0*1.15^2\\ ...\\ a_n=a_0*1.15^n\\ a_n \geq 3*a_0\\ 1.15^n \geq 3\\ n*ln(1.15) \geq ln(3)\\ n \geq \dfrac{ln(3)}{ln(1.15)} \\ n \geq 7.86059688...\\\\ \boxed{n \geq 8}$