SOLUTION: I'm struggling to answer this question. Can I please get some help? I would really appreciate. The sales of a new electronic gadget are growing exponentially such that a total

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Question 809893: I'm struggling to answer this question. Can I please get some help? I would really appreciate.
The sales of a new electronic gadget are growing exponentially such that a
total of 10000 gadgets were sold in 2000 and 82700 gadgets were sold in
2002. If this trend continues, in what year will sales of the gadget reach or
exceed 500 000?
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
y=Ae%5E%28kx%29
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%28y%29=ln%28A%29%2Bln%28e%5E%28kx%29%29
ln%28y%29%2Fln%28A%29=kx%28ln%28e%29%29
ln%28y%29%2Fln%28A%29=kx%2A1
k=%28ln%28y%29%29%2F%28x%2Aln%28A%29%29
Substitute the coordinates from the data point.
k=ln%2882700%29%2F%282%2Aln%2810000%29%29
highlight%28k=0.615%29

The model equation to use is then highlight%28y=10000%2Ae%5E%280.615%2Ax%29%29

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