A person invests $1,150 in an account that earns 5% annual interest compounded continuously. Find when the value of the investment reaches $2,000. If necessary round to the nearest tenth.The investment will reach a value of $2,000 in approximately_____years.

Answer:11.1 yearsStep-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 withln(1.739130435)=.05tTaking the natural log of that decimal on our calculator gives us.5533852383=.05tNow divide both sides by .05 to get t = 11.06770477 which rounds to 11.1 years.