Find the rabbit and fox population as a function of time full#

Find the rabbit and fox population as a function of time full#

Um Okay so we can now take equation A in its full form and find out when the rabbits go extinct. Now that may not be such a problem but but then the foxes would have an issue so yeah everything's it's related. And of course we're worried now about the rabbits going extinct. Okay so then we can finally write down our full rabbit as a function of time formula. Coleslaw Algorithm, a five or K is log 5/5 and I'll convert that to decimal real quick. So the exponent function goes away And we're left with 5K. The algorithm is the opposite of the exponential function. And that's just five and we take the longer than both sides. 5K over by itself is 1700 minus 1200 over 100. Um So it'll take some algebra but let's see, pull the feet of the K.

Okay so then we can put that in 1200 Is equal to 1700 minus 100 Times E. So yeah, whatever control seems to be working. So there are 1200 rabbits after five years. So we can solve for a it is 100 then we are given another data point five years later equal five years We're told is are at five is one quarter less. And so if we put that in our of zero is 1700 minus A. Okay, so the first thing we know is that The rabbit population time T equals zero is 1600. Is found from another data point on the rabbit population. Is typically found from initial conditions and K. And try to determine the unknown parameters.

An equation be the first thing to do is take equation A. But anyway we are going to look at some things about these two equations and we'll call them equation A. It's probably the way I would phrase that and I don't see that interrelation and I should say when they're coexisting in the same resource area. And finally overall the most unrealistic thing is that the two um populations of fox and rabbits do not have have coupled equations and I would say that's probably the biggest concern is whenever you have species interacting in a certain region, especially when they depend so um precariously I'll say on each other once a food source for the foxes and of course the foxes are a source of death for the rabbits, you would expect a couple of equations that would determine the number in each, dependent on the number and the other and that's something really big that's missing. There are usually things that take out the population, there are resource limitations that create what's called a logistic curve. So whenever you have the rate of change in a population directly proportional just to that population that is just exponential growth. Um The second thing that looks a little bit fishy is the fox ah equation two, fox is just show exponential growth. And the other thing that looks a little bit unclear is um what about resource limitations and disease and hunting and you know, other things that could take out the population or cause it to um change. So the negative part there at the end and we it's not clear how the rabbits are reproducing. Says that the rabbit population is just decreasing um according to at the part due to the foxes.

So I'll just denote those from the start because this looks like an incomplete model in many ways, I won't say incorrect because somebody's probably starting with so modeling or numbers that they've collected in the field.

And there are a couple of things that I would like to start off and say look very unrealistic with this model. The top equation governs the number of rabbits in the region and the bottom one is going to govern the number of foxes. So we are looking at a population model in a certain forest for the number of rabbits R. Population models usually involve some mathematical relationships that tell us how many of a certain species exist in a region at a given time.