I need help working problem 1 using separation of fractins. I worked out part of it but not sure if it is correct and what to do next! Please help and show all steps and methods please!
Mlle Allee Effect by Jo Gascoigne The top five most famous Belgians apparently include a cyclist a punk si ventor of the saxophone, the creator of Tintin. and Audrey Hepburn. Pierre i Verhulst is not on the list. although he should be. He had a fairly short life. dying al the age of 45, but did manage to include some excitement- he was deported from Rome for trying to persuade the Pope that the Papal Stat needed a written consti tion. Perham the Pope knew better even then than t tak lecture in ps nance from a Belgian Aside from this episode, Pierre Verhulst was a n concerned himself, among other things, with the dynamics ie is on the left fish, rabbits, buttercups, bacteria, of natural of lish, so we will be thinking or whatever. am prejudiced favour tions had up to this fish from now on.) Theorizing in natural popul obvious point been on the growth of reached the conclusion relatively limited, although scientists had Population size a that the growth rate of a population (dN/dt, where N is the both ime depended on (i the birth rate b and (i) the mortality rate m of which would vary in direct proportion to the size of the population N mN. After combining b and m into one parameter r, called the intrinsic rate of natural increase-or more usually by biologists without the time to get their around that, just r- equation (1) becomes tongues This model of population growth has a problem, which should be clear to you-if not, plot dN/dt for increasing values of N. It is a straightforward exponential growth curve, suggesting that we will all eventually be drowning in fish. Clearly, something eventually has to step in and slow down dN/dt, Pierre Verhulst's insight was that this something was the capacity of the environment, in other words How many fish can an ecosystem actually support? r He formulated a differential equation for the population NO) that included both and the carrying capacity K r 0 (3) of ation (3) is called the logistic equation, and it forms to this day the basis of much the modern science of population dynamics. Hopefully, it is clear that the N/Ko, which is Verhulst's contribution to equation (2), is N/K) 1 when N 0, leading to exponential growth, and (1 N/k) 0 as N K., hence it causes. the growth curve of N(t to approach the horizontal asymptote Noto K. the size Thus of the population cannot exceed the canying capacity of the environment.
