Question

A country x has a population growth rate of 3%. how many years will it take the population of country x to double? use continuous compound growth

Answer 1

$A=Pe^{rt}$
A=future amount
P=present amount
r=rate in decimal
t=time in years

so
when will A=double of original?
or when will A=2P

r=3%=0.03
t=t

$A=Pe^{(0.03)t}$
$2P=Pe^{0.03t}$
divide both sides by P
$2=e^{0.03t}$
take ln of both sides
$ln(2)=ln(e^{0.03t})$
$ln(2)=0.03t ln(e)$
$ln(2)=0.03t (1)$
ln(2)=0.03t
divide both sides by 0.03
(ln(2))/0.03=t
use calculator
23.1049=t
so a little over 23 years, about 23 years and 38.2 days