Simple business question.
There are 6500 products which are expired in 11 months. Right now we are selling 300 items per month.
Which is the growth factor of our sells we need to achieve to sell them all before they are expired?
I guess the best way to start is to define the growth factor r
So: ∑ 300 * (1 + r)^11 = 6500
How could I write it in a calculator? :)
Your sum is not quite correct, it also has no summation index. You want $$\sum_{k=0}^{10} 300\cdot (1+r)^k=6500.$$ Note this is assuming that growth starts in the second month, i.e. you sell $300$ in the first month, and it increases after that. If growth starts in the first month your series would run from $1$ to $11$. Simplifying your equation we have $$\sum_{k=0}^{10} (1+r)^k = \frac{65}{3}.$$ This is a geometric series. Therefore $$\frac{(1+r)^{11}-1}{r}=\frac{65}{3}.$$ I really don't think there is much hope for an analytic solution from here. I got $r\approx0.1288$ or $12.88$ per cent growth per month.