Why does logistic growth look like exponential?

An exponential growth occurs when growth rate of a value of a mathematical function is proportion 

The Red Sea Rift is a divergent boundary between the Arabian and African Plates. It is a rift that is causing sea floor spreading and the expansion of the Red Sea. The Red Sea Rift itself is mostly useless because of the fact it is submerged underwater. However the Red Sea is a sea surrounded by people, who use it often. It has several volcanoes and a few of them are active.