Question 809893
{{{y=Ae^(kx)}}}
y is amount of sales, how many of the gadget sold,
A is initial amount sold at beginning reference time, arbitrarily at x=0
k is a constant
x is time in years since year 2000.


The description indicates A=10000, which is for x=0, same as year 2000.


Data point, (x,y), (2, 82700) will allow us to find k.
Solve for k from the general equation first:
{{{ln(y)=ln(A)+ln(e^(kx))}}}
{{{ln(y)/ln(A)=kx(ln(e))}}}
{{{ln(y)/ln(A)=kx*1}}}
{{{k=(ln(y))/(x*ln(A))}}}
Substitute the coordinates from the data point.
{{{k=ln(82700)/(2*ln(10000))}}}
{{{highlight(k=0.615)}}}


The model equation to use is then {{{highlight(y=10000*e^(0.615*x))}}}


Question --- y=500000?  What is x?  
Just start with the found model equation, solve for x, and plug-in the value given for y.