Question 133494
{{{A=Pe^(rt)}}} Start with the given equation



{{{15000=5000e^(0.0485t)}}} Plug in {{{A=15000}}}, {{{P=5000}}}, {{{r=0.0485}}}



{{{ln(15000)=ln(5000e^(0.0485t))}}} Take the natural log of both sides



{{{ln(15000)=ln(5000)+ln(e^(0.0485t))}}} Break up the natural log on the right side



{{{ln(15000)-ln(5000)=ln(e^(0.0485t))}}} Subtract {{{ln(5000)}}} from both sides



{{{ln(15000)-ln(5000)=0.0485t*ln(e)}}} Rewrite the right side using the identity  {{{ln(x^y)=y*ln(x))}}}


{{{ln(15000)-ln(5000)=0.0485t*1}}} Evaluate {{{ln(e)}}} to get 1



{{{ln(15000)-ln(5000)=0.0485t}}} Multiply 



{{{(ln(15000)-ln(5000))/0.0485=t}}} Divide both sides by 0.0485 to isolate t



Using a calculator, we get


{{{t=22.6517998}}}



So it takes about 22.65 years for $5000.00 to grow to $15,000.00