Question 1076016

{{{y=y[0]e^(kt)}}} , give the exact value of {{{k}}} in terms of natural logarithms

{{{y[0]=70}}}, 
{{{t=110}}}, 
{{{y=35}}}
{{{k}}}=? 


{{{35=70e^(k*110)}}}


{{{35/70=e^(110k)}}}


{{{1/2=e^(110k)}}} .........take natural logarithms


{{{ln(1/2)=ln(e^(110k))}}}


{{{ln(1)-ln(2)=(110k)ln(e)}}}........since {{{ln(e)=1}}} and {{{ln(1)=0}}}, we have


{{{-ln(2)=110k}}}


{{{k=-ln(2)/110}}}