Invasive species often display a wave of advance as they colonize new areas. mathematical models based on random dispersal and reproduction have demonstrated that the speed with which such waves move is given by the expression 2 dr , where r is the reproductive rate of individuals and d is a parameter quantifying dispersal. calculate v'(r), the derivative of the wave speed with respect to the reproductive rate r.

Ireally just need to get finished with precal! i’m really sorry i have to do this! hope this !

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All these statements are related to drake's equation. it is a probabilistic equation that shows an aproximate number of civilizations in our galaxy that we can communicate with. all the numbers that are inserted into equation are not precisely known so the result varies from 1000 to 100,000,000. the equations was not created to calculate exact number of extraterrestrial civilizations but to increase scientific knowledge how to find them.the equation is: where: n=  represents the number of civilizations in our galaxy that we could in principle communicate with today.  the average rate of  star formation  in  our galaxy  the fraction of those stars that have  planets  represents the number of planets in the galaxy that are in principle capable of having surface liquid water and life.  essentially represents the probability that life eventually arises on a habitable planet.  represents the number of life-bearing planets in the galaxy.  epresents the total number of planets on which intelligent beings have evolved and developed a communicating civilization at some time in the galaxy's history.    essentially represents the probability that on a planet with life, some organisms will eventually evolve to the point where they can build radio telescopes.    is a factor that depends on how long civilizations that reach our level of technology are able to survive.