## 2013-10-05

### Pyramid (exponential) Power (1)

When I walked down a street, I was thinking about creating an exponent exercise for my math class. I sometimes just get inspired an idea when I walk down a street. My main purpose is to show how fast the exponential can grow.

Hitoshi has no money, so he wants to join a pyramid system. The system asked to him to buy something 1,000 Euro every month from the company. But, if he has 40 people for his next level, and the next level has 40 people each, he can get some commission from 25% of two levels lower's people's purchase. When he got the money, he also need to pay 10% to the higher level. Berlin is quite new for this system, so there are only founder (level 1) and co-founders(level 2), 41 people are there. Assume Berlin has 2.5 million people.

1. How much money Hitoshi can get every month? Assume Hitoshi can convince even everyone in Berlin.
2. Hitoshi asked to join his friend Daniel, to be his next level person. How much money Daniel can get?
3. How many people must be convinced that Hitoshi get money in Berlin?

The answer will be in the next post.