IB MAI HL Calculus Topic 5.4 Differential Equations (id: 5c7b55dd4)

本题目来源于试卷: IB MAI HL Calculus Topic 5.4 Differential Equations，类别为 IB数学

[填空题]
A marine biologist is studying the population growth of a pey;w gc+0 f+vcdngu+ag d pcyr swl2p:f+*;in colony in a small archipelago that is free from predators. At the start of her study, there was estimated to be 200 penguins in the colony. It is assumed the population growth of penguins can be modelled by thcw:f+ y+lp;a2dprgs *e differential equation

$\frac{\mathrm{d} P}{\mathrm{~d} t}$=1.1 P

where P is the penguin population at time t years.
1. Find the population of penguins after 3 years.
After 3 years there are approximately    penguins
​

When the population of penguins reaches 5000 , it is noticed that a group of 100 leopard seals have settled in the area. The subsequent population growth of penguins and leopard seals, where L is the population of leopard seals at time t , can be modelled by the coupled differential equations

$\frac{\mathrm{d} P}{\mathrm{~d} t}$=P(2.2-0.011 L) $\quad \frac{\mathrm{d} L}{\mathrm{~d} t}$=$L(0.0002 P-0.7)$

2. Using Euler's method with a step size of 0.25 , estimate
1. the population of penguins 1 year after the leopard seals were noticed;
After 1 year there are approximately    penguins
2. the population of leopard seals 1 year after they were noticed.
After 1 year there are approximately    leopard seals
​

The graph of the population sizes, according to this model, for the first 4 years after the leopard seals were noticed is shown below.

3. Describe the changes in the populations of penguins and leopard seals for these 4 years,
1. at point A ;
2. at point B .
4. Find the non-zero equilibrium point for the populations of penguins and leopard seals.
therefore the non-zero equilibrium point is
P(  ,  )
​

参考答案:
空格1: 5420  空格2: 11000  空格3: 197  空格4: 3500  空格5: 200 


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