Question 64971
THE AMOUNT A IN AN ACCOUNT AFTER t YEARS FROM AN INITIAL PRINCILE P INVESTED AT AN ANNUAL RATE r COMPOUNDED CONTINUOUSLY IS GIVEN BY A=Pe^rt WHERE r IS EXPRESSED AS A DECIMAL.  HOW MANY YEARS WILL IT TAKE AN INITIAL INVESTMENT OF $1,000 TO GROW TO $1,700 AT THE RATE OF 4.42% COMPOUNDED CONTINUOUSLY? 
A=1700
P=1000
r=4.42/100=.0442
{{{1700=1000e^(.0442t)}}}
{{{1700/1000=1000e^(.0442t)/1000}}}
{{{17/10=e^(.0442t)}}}
{{{ln(17/10)=ln(e^.0442t)}}}
{{{ln(17/10)=.0442tln(e)}}}
{{{ln(17/10)=.0442t(1)}}}
{{{ln(17/10)=.0442t}}}
{{{ln(17/10)/.0442=.0442t/.0442}}}
{{{ln(17/10)/.0442=t}}}
{{{12.00516405=t}}}
{{{highlight(t=12)}}} yrs.
Happy Calculating!!!