Answer:
Step-by-step explanation:
When the interest compounds continuously, our formula is
[tex]A(t)=Pe^{rt}[/tex]
If we start with 10000 and are looking for how long, t, it takes to double, we are looking for how long it will take for our account to have 2 times 10000. That's 20000. Therefore, our equation is
[tex]20000=10000e^{.11t}[/tex]
Divide both sides by 10000 to get
[tex]2=e^{.11t}[/tex]
Take the natural log of both sides to "undo" that e:
[tex]ln(2)=ln(e^{.11t})[/tex]
Again, since ln and e undo each other what we have now is
ln(2) = .11t and
[tex]\frac{ln(2)}{.11}=t[/tex] so
t = 6.3 years
