Question 1010020

{{{P(t)=1+ke^(0.08t) where {{{k}}} is a constant and {{{t}}} is the time in years.  
{{{k=37000}}} 
{{{P(t)= 92500}}}

find: {{{t}}}

{{{92500=1+37000e^(0.08t)}}}


{{{92500-1=37000e^(0.08t)}}}


{{{92499=37000e^(0.08t)}}}


{{{92499/37000=e^(0.08t)}}}


{{{2.499972972972973=e^(0.08t)}}}........take a natural log of both sides


{{{ln(2.499972972972973)=ln(e^(0.08t))}}}


{{{ln(2.499972972972973)=(0.08t)ln(e)}}}-----{{{ln(e)=1}}}


{{{ln(2.499972972972973)=0.08t


{{{t=ln(2.499972972972973)/0.08}}}


{{{t=0.9162799210049070/0.08}}}


{{{t=11.4534990125613375}}}


{{{t=11.5}}}->{{{t}}}={{{11}}}{{{1/2}}} years