Question 703336


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



{{{700=100*e^(0.09*t)}}} Plug in {{{A=700}}}, {{{P=100}}}, and {{{r=0.09}}} (the decimal equivalent of 9%).



{{{700/100=e^(0.09*t)}}} Divide both sides by {{{100}}}.



{{{7=e^(0.09*t)}}} Evaluate {{{700/100}}} to get {{{7}}}.



{{{ln(7)=ln(e^(0.09*t))}}} Take the natural log of both sides.



{{{ln(7)=0.09*t*ln(e)}}} Pull down the exponent using the identity {{{ln(x^y)=y*ln(x))}}}.



{{{ln(7)=0.09*t*1}}} Evaluate the natural log of 'e' to get 1.



{{{ln(7)=0.09*t}}} Multiply and simplify.



{{{1.94591014905531=0.09*t}}} Evaluate the natural log of {{{7}}} to get {{{1.94591014905531}}} (this value is approximate).



{{{1.94591014905531/0.09=t}}} Divide both sides by {{{0.09}}} to isolate 't'.



{{{21.6212238783924=t}}} Evaluate {{{1.94591014905531/0.09}}} to get {{{21.6212238783924}}}.



{{{t=21.6212238783924}}} Flip the equation.



{{{t=22}}} Round to the nearest whole year.


So it will take about 22 years.