The differential equation can be solved by elementary (if tedious) methods. We find The survival probability is If the death rate is greater than the
{"Image DocumentName": "The differential equation can be solved by elementary (if tedious) methods. We find", "Image ImageDescription": "The survival probability is. If the death rate is greater than the birth rate ( \u03b3>\u03b2) the population will die out exponentially. If \u03b3<\u03b2 the long time survival probability is. If \u03b3=\u03b2 the expression for the survival probability is undetermined, but we can work out the limit. At the critical point \u03b2=\u03b3 the population decays by a power law with exponent -1.", "Image XResolution": "37", "Image YResolution": "37", "Image ResolutionUnit": "Pixels/Centimeter", "Image Software": "SlidePlayer", "Image YCbCrPositioning": "Centered"}