Question 1205115

This formula says, when an amount{{{ P}}} is invested for the time '{{{t}}}' with the interest rate is {{{r}}}% compounded continuously, then the final amount is, 

{{{A = P *e^(rt)}}}


The initial amount is {{{P = 2000}}}.
The interest rate is, {{{r = 5}}}% = {{{5/100 = 0.05}}}
The amount after {{{t }}}years ={{{4500}}}
Time is, {{{t}}}=?


{{{4500 = 2000* e^(0.05t)}}}

{{{4500/2000=e^(0.05t)}}}

{{{e^(0.05t)=9/4}}}....take natural log of both sides

{{{ln(e^(0.05t))=ln(9/4)}}}

{{{(0.05t)ln(e)=ln(9)-ln(4)}}}...{{{ln(e)=1}}}

{{{0.05t=2.19722-1.386294361}}}

{{{0.05t=0.810925639}}}

{{{t=0.810925639/0.05}}}

{{{t=16.2}}}

it will take her {{{16.2}}} years for money to grow to the ${{{4500 }}}