Here is the question. I've spent about ten hours trying to get this to work, but I just can't crack it. I've changed the numbers to try and keep it simple. I can't really seem to find any similar questions on the net.
A jewelry firm sells 1000 pieces of jewelry in its first month. If sales increase at a rate of 5% a month, how long will it take to sell 15 000 products in total?
Here's what I know. It's geometric progression, as the topic title suggests, and the number is larger than one, so the formula is:
Sn = a((r^n)-1)/(r-1)
Which will look like:
15000n = 1000((1.05^n)-1)/(1.05-1)
I've worked out how long it will take to be sell 15000 a month (by accident) and I even know what n should be (about 11.5 months) but I can't find a mathematical method to prove it. I think the next step should be:
log(15000)n = 1000 + log((1.05^n)-1) - log(1.05-1)
But even if that is right, I'm not sure how to solve it because of the ^n on the right hand side of the equation.
Any help on this matter would be much appreciated.