Question 1198609
{{{A = P e^(rt)}}}

If the initial population is {{{1}}} unit, then in {{{5.48 }}} years the population will be {{{2}}} units.

{{{2 = 1*e^(5.48r)}}}

Take the natural logarithm of both sides:

{{{ln(2)  = ln(1* e^(5.48r))}}} 

{{{ln(2)  = ln(1)+ln(e^(5.48r))}}}
 
{{{ln(2) =0+ 5.48r*ln(e)}}}

{{{ln(2) =5.48r*1}}}

{{{r = ln(2)/5.48}}}

{{{r = ln(2)/5.48}}}

{{{ r =0.126487}}}........per year, exactly 

or

{{{r }}}≈ {{{12.6487}}}%........ per year