The basic equation for continuous compounding is as follows:
[tex]A=Pe^{rt}[/tex]
Plugging in the given values gives:
[tex]10000=5000e^{0.027t}[/tex]
Dividing both sides by 5000, we get:
[tex]2=e^{0.027t}[/tex]
Take natural logs of each side:
[tex]ln\ 2=0.027t[/tex]
from which we find that t = 25.67 years.
