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For each of the following Leslie matricesl , assume that the initial population is large enough s0 that the eventual long-term population growth (o decay) and age d...

Question

For each of the following Leslie matricesl , assume that the initial population is large enough s0 that the eventual long-term population growth (o decay) and age distribution become apparent, (i.e , if the population is decaying; You may assume that that its long-term behavior becomes clear before the population vanishes) Find the long-term rate of growth or decay. ji. Find the eventual distribution of juveniles (J) and adults (A) as proportion of the entire populationA J [0.7 0.9 (a) A| 1.6 0A

For each of the following Leslie matricesl , assume that the initial population is large enough s0 that the eventual long-term population growth (o decay) and age distribution become apparent, (i.e , if the population is decaying; You may assume that that its long-term behavior becomes clear before the population vanishes) Find the long-term rate of growth or decay. ji. Find the eventual distribution of juveniles (J) and adults (A) as proportion of the entire population A J [0.7 0.9 (a) A| 1.6 0 A J [ 0.7 0.2 (6) A | 0.2 0.4 A J [0.5 1.4 A| 0.9 0 J A J [0.1 1.2 (d) A | 0.4 0.3



Answers

Solve the logistic differential equation representing population growth with the given initial condition. Then use the solution to predict the population size at time $t=3$. $y^{\prime}=y(1-y), y(0)=0.5$

From a number 19 So part a p prime is a good A 0.1 pft. Then we got P zeros you go to to okay is a good A 0.1 pft is you goto p zero e to the k t So we ride up Pft is to go toe to e to the 0.1 t Yeah the party initial population in 2015 waas two million because we put into equals zero and we get to million part C. It was in 19 corresponds to tickles for PF four equals to e to the 0.4 which comes out to 2.816 million.

Hello, everyone. Today we're going to solve a problem. Number 25 here. DP by the the minus can't beat equals. And so p off t equals minus que onda que off t equals integrating factory coz e integral minus k duty which is equal to us to mine escaping. So because you know the power Katie Integral and it is a power minus Katie duty so b equals evil about Katie minus end by K into the pole minus Katie plus C so p will be equal toe minus and different by K plus C to the power. Katie, this is General solution. So at T equals zero be equal. Do be not so P note will be called tau minus and they were a big K plus c u to the power zero. So sequel toe be not plus and developed by k p equal to minus endeavored by K plus Be not plus and they were a big K. It is too, Katie. So period eyes equal toe dp by d p which is equal to be not care plus and in tow. The power Katie. Thank you

Problem for 34 The population of the state two years after Ah 2010 is given by function. Why cause PT with growth constant so from a party? So from the graph, you can see that 10 physical to 10.5 million then, for we want to find pft once, ah, population to go with 10 million and you can see that it's looking at the graph. It's t equals eight years. Part c Want to find the derivative PT which is 0.25 pft. We know that the derivative ah, 10 million year or 10 years after is 100.25 you have 10 which is 0.25 times 10.5 which is equal to 0.26 to 5. Therefore, it's 2,262,000 people per year in party. So we said 10 to some five. You go to 0.25 10 pft soft P t s a p F T is you got 11 and weaken. Then figure out that in order for PST equal to 11, looking at the graph you have t is equal to 11

So for this problem we have the Census Bureau and we know that um the estimated growth rate of K of the world population will decrease by roughly uh 0.2 per year for the next few decades. So in 2000 and four, K was 40.132 So we want to express K as a function of time. So we see that K um equals originally it was 0.132 And it's a decreasing at a rate of 0.2 T. So you see, it's decreasing over time. Um since 2000 and four were t equals zero. And we could find a differential equation that models the population for this problem. Um And we were just multiplied this whole thing right here because this is the rate we would just multiply this times. Why? That was the R D Y G. All right. There is going to be our final answer. And then we could solve this differential equation and graph it using the methods that we've discussed earlier.


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