That you would see, when the population is wellīelow that carrying capacity, is reasonable to model it Natural maximum carrying capacity that the environment can actually sustain. Infinite number of rabbits or you can't just grow forever. Growing by the input, which is time, is being It called exponential growth? Well you notice, we are Here, is exponential growth, exponential growth, and why is And so what's more likely to happen, what we described right over Maximum carrying capacity for certain part of the environment for a certain type of species. There are no predators, or competition for resources. Is that there is not infinite food and infinite space, and it isn't the case that Saying if they have enough food and if they have enough space. Reproduce long enough, they would frankly take over the planet, if they had enough food and It's gonna have this kinda hockey stick j shape right over here. Or this type of equation, let me see population I, population, this is an exponential function, and so your populationĪs a function of time is gonna look like this, Let's say in months, and this axis you have your population, you have your population. Something like this out, if you were to plot the rabbit population with respect to time, you would see a graph that Space or predators or food, and if you were to plot And so you quickly realizeġ0% per month is quite fast, and this might seem extremely fast, but it's actually not outlandishįor a population of rabbits that are not limited by Of 93,000 over 10 years, so over another 10 years, we're gonna grow by 93,000 times this. So we started with 1,000,Īnd we're gonna have approximately 93 million To be equal to roughly 93 million rabbits, Population, so times 1,000, one two three, is going Power is equal to that, times our original I can not calculate one point one to the 120th power in my head. One to the 120th power, and so let's, let me get aĬalculator out to do that. Of 120 months is gonna be 1,000 times one point Getting crazy numbers", but just for kicks, let's just think about what's gonna happen in 10 years. And you might say, "Okay this makes sense, "it doesn't look like we're Our initial population, our initial population, Of n, as a function of n, is gonna be equal to And so we can set up an expression here, we can say look the population, let's say that the population is P. Times, or being multiplied by one point one n times, or 1,000 times one point N months into the future, well you can see what's going to be. One to the third power, we're just gonna multiplyīy one point one again. Population's gonna be 1,000 times one point Month, which was that, which we have right over there, but then we're gonna multiplyīy one point one again, or we can just say this Gonna be the population that we started at theīeginning of the month times one point one again, so it's gonna be the population at the beginning of the So we can multiply it by one point one, and that math we can do in our head, it is 11 hundred, or 1,100, but let's just write thisĪs 1,000 times one point, not one point five, times one point one. You have your original population, and then you grow it by 10%, That's the same thing as multiplying by one point one. Well, our population's gonna grow by 10%, so we can take our populationĪt the beginning of the month, and growing by 10%, Information given to us, that at zero months, we're Let's just say this is the number of months that have gone by, and on the right column, let's
So let's set up a little bit of a, let's set up a little How that population will grow, if it's growing 10% per month. Rabbits, and we know that this population is That we're starting with a population of 1,000
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