Question 600259


{{{A=Pe^(rt)}}} Start with the continuous compounding formula.



{{{200=100*e^(0.06*t)}}} Plug in {{{A=200}}}, {{{P=100}}}, and {{{r=0.06}}} (the decimal equivalent of 6%).



{{{200/100=e^(0.06*t)}}} Divide both sides by {{{100}}}.



{{{2=e^(0.06*t)}}} Evaluate {{{200/100}}} to get {{{2}}}.



{{{ln(2)=ln(e^(0.06*t))}}} Take the natural log of both sides.



{{{ln(2)=0.06*t*ln(e)}}} Pull down the exponent using the identity {{{ln(x^y)=y*ln(x))}}}.



{{{ln(2)=0.06*t*1}}} Evaluate the natural log of 'e' to get 1.



{{{ln(2)=0.06*t}}} Multiply and simplify.



{{{0.693147180559945=0.06*t}}} Evaluate the natural log of {{{2}}} to get {{{0.693147180559945}}} (this value is approximate).



{{{0.693147180559945/0.06=t}}} Divide both sides by {{{0.06}}} to isolate 't'.



{{{11.5524530093324=t}}} Evaluate {{{0.693147180559945/0.06}}} to get {{{11.5524530093324}}}.



{{{t=11.5524530093324}}} Flip the equation.



{{{t=12}}} Round to the nearest whole year.



So it will take 12 years.