Question 866914
NOT this, <i>N = 100 ekt,</i>
but THIS:  {{{N=100e^(kt)}}}.


You want to first find what is k.
{{{ln(N)=ln(100)+kt*1}}}
{{{kt=ln(N)-ln(100)}}}
{{{highlight_green(k=(1/t)ln(N/100))}}}
Substituting the given data from the description,
{{{k=(1/3)ln(150/100)}}}
{{{k=(1/3)ln(1.5)}}}
{{{highlight_green(k=0.135)}}}


Now you have the model as {{{highlight(N=100e^(0.135t))}}}.


Remember this:{{{kt=ln(N)-ln(100)}}}
Now, since you want to know t for when N=200, solve for t, ...
{{{t=(1/0.135)(ln(200/100))}}}