Exponential distributionIn probability theory and statistics, the exponential distribution or negative exponential distribution is the probability distribution of the time between events in a Poisson point process, i.e., a process in which events occur continuously and independently at a constant average rate. It is a particular case of the gamma distribution. It is the continuous analogue of the geometric distribution, and it has the key property of being memoryless. In addition to being used for the analysis of Poisson point processes it is found in various other contexts.
Macroscopic scaleThe macroscopic scale is the length scale on which objects or phenomena are large enough to be visible with the naked eye, without magnifying optical instruments. It is the opposite of microscopic. When applied to physical phenomena and bodies, the macroscopic scale describes things as a person can directly perceive them, without the aid of magnifying devices. This is in contrast to observations (microscopy) or theories (microphysics, statistical physics) of objects of geometric lengths smaller than perhaps some hundreds of micrometers.
Characterizations of the exponential functionIn mathematics, the exponential function can be characterized in many ways. The following characterizations (definitions) are most common. This article discusses why each characterization makes sense, and why the characterizations are independent of and equivalent to each other. As a special case of these considerations, it will be demonstrated that the three most common definitions given for the mathematical constant e are equivalent to each other.
Lake KivuLake Kivu is one of the African Great Lakes. It lies on the border between the Democratic Republic of the Congo and Rwanda, and is in the Albertine Rift, the western branch of the East African Rift. Lake Kivu empties into the Ruzizi River, which flows southwards into Lake Tanganyika. In the past, Lake Kivu drained toward the north, contributing to the White Nile. About 13,000 to 9,000 years ago, volcanic activity blocked Lake Kivu's outlet to the watershed of the Nile.
