Question 811763
Take year 2000 to be time of 0, for convenience.


{{{y=10000e^(kt)}}}  for t as time in years since 2000, y is the sales count of items sold at time t, and k is a constant.


Solve symbolically for k.
{{{ln(y)=ln(10000)+kt*ln(e)}}}
{{{ln(y)-ln(10000)=kt}}}
{{{k=(ln(y)-ln(10000))/t}}}


Use the point for year 2002, for t=2, to get a value for k.
{{{k=(ln(82700)-ln(10000))/2}}}
{{{k=2.1126/2}}}
{{{highlight(k=1.056)}}}


The model equation is {{{highlight(y=10000e^(1.056*t))}}}-----


Your question to answer is, find t for y=500000.
Looking back at solving for k, the step was found,
{{{ln(y)-ln(10000)=kt}}}
from which we can easily step to 
{{{t=(ln(y)-ln(10000))/k}}}
and then substituting for y, and k,
{{{t=(ln(500000)-ln(10000))/1.056}}}
{{{highlight(t=3.704)}}} years since 2000, or some late in the year 2003, or very early in year 2004.


Think about that time value.  2000+3.7=2003.7, which could potentially be early in year 2004.