[tex]A=Pe^{rt}[/tex]
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
[tex]A=Pe^{(0.03)t}[/tex]
[tex]2P=Pe^{0.03t}[/tex]
divide both sides by P
[tex]2=e^{0.03t}[/tex]
take ln of both sides
[tex]ln(2)=ln(e^{0.03t})[/tex]
[tex]ln(2)=0.03t ln(e)[/tex]
[tex]ln(2)=0.03t (1)[/tex]
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
