Logistical growth

1. Exercise:

On an island with 2000 inhabitants one of the inhabitants falls ill with the incurable disease lusteriosis. This disease is never fatal, but it is so highly infectious that if you meet a sick person, the healthy person is infected in any case.

On the island, each inhabitant meets another inhabitant on average every hour.

Describe the spread of the epidemic in a graph.

2. Exercise:

A bacterial culture starts growing at 8% per minute. The initial population is 100 bacteria. However, there is only food for a maximum of 10000 bacteria, so the increase is proportional not only to the number of bacteria present, but also to the available food.

3. Exercise:

There is a market of 250000 buyers for a commodity. The product is so good that everyone who knows the product buys it and tells their friends about it. In order to bring the product into circulation, the company gives away 1000 times this commodity. In the first month a turnover of 100 pieces is registered. After how many months can the company expect to reach half of the market?