Llayden
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"If in the exponential model for population growth, dy/dt=ry, the constant growth rate r is replaced by a growth rate r(1-y/k) that decreases linearly as the size of the population increases, we obtain the logistic model for population growth,
dy/dt = ry (1 - (y/k)),
in which K is referred to as the carrying capacity of the population. Sketch the graph of f, find the critical points, and determine whether each is asymptotically stable or unstable."
This should be really simple and straight forward (only looking for graphs of dy/dt vs t, phase line, and solution graph) but it is tripping me up a bit. I think I've found the critical points (y=0,k)? I'm also having an issue trying to graph this function. It's quadratic, is it not?
dy/dt = ry (1 - (y/k)),
in which K is referred to as the carrying capacity of the population. Sketch the graph of f, find the critical points, and determine whether each is asymptotically stable or unstable."
This should be really simple and straight forward (only looking for graphs of dy/dt vs t, phase line, and solution graph) but it is tripping me up a bit. I think I've found the critical points (y=0,k)? I'm also having an issue trying to graph this function. It's quadratic, is it not?