A simple but useful method of analysis of hyperbolic processes is presented and its application is illustrated by using the growth of human population in Africa, the economic growth in Western Europe and the examination of the fundamental postulates of the Unified Growth Theory. It is shown how this method can revolutionize the interpretation of the historical economic growth and the growth of human population and how it can help to understand the current growth. Examples used to illustrate the application of this method show that, contrary to the accepted interpretations, the Industrial Revolution and the accompanying unprecedented technological development had no impact on the economic growth even in Western Europe and that Galor’s Unified Growth Theory fails the scientific test.