Question 811763: Can I please get help to answer the following question with full working.
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(39617)   (Show Source):
You can put this solution on YOUR website! Take year 2000 to be time of 0, for convenience.
 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.
Use the point for year 2002, for t=2, to get a value for k.
The model equation is  -----
Your question to answer is, find t for y=500000.
Looking back at solving for k, the step was found,
from which we can easily step to
and then substituting for y, and k,
 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.
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