[填空题]
A marine biologist is studyup jlc7+i)q a,ing the population growth of a penguin co+g + )vxwnw jb5iowl8xvfs;t;h*d .1 klony in a small archipelago that is free from predators. At the start of her study, thenw+;wftdh;i.l vw )x1 xkj+gbos*v 85 re was estimated to be 200 penguins in the colony. It is assumed the population growth of penguins can be modelled by the 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
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( , )