Answer:
11.1 years
Step-by-step explanation:
The formula for interest compounding continuously is:
[tex]A(t)=Pe^{rt}[/tex]
Where A(t) is the amount after the compounding, P is the initial deposit, r is the interest rate in decimal form, and t is the time in years. Filling in what we have looks like this:
[tex]2000=1150e^{{.05t}[/tex]
We will simplify this first a bit by dividing 2000 by 1150 to get
[tex]1.739130435=e^{.05t}[/tex]
To get that t out the exponential position it is currently in we have to take the natural log of both sides. Since a natural log has a base of e, taking the natual log of e cancels both of them out. They "undo" each other, for lack of a better way to explain it. That leaves us with
ln(1.739130435)=.05t
Taking the natural log of that decimal on our calculator gives us
.5533852383=.05t
Now divide both sides by .05 to get t = 11.06770477 which rounds to 11.1 years.
