Whats the answers to D and E? D has 5 choices Populations of aphids and ladybugs

Question

Whats the answers to D and E? D has 5 choices

Populations of aphids and ladybugs are modeled by the equations 2A 0.01 AL 0.5L +0.0001AL dt (a) Find the equilibrium solutions (Enter solutions from smallest to largest value of A (A, L) 0 (A, L) 5,000 200 (b)Find an expression for dL/dA. 5L .0001AL. dL/dA 2A 01AL. (c) The direction field for the differential equation in part (b) is shown. Use it to sketch a phase portrait. What do the phase trajectories have in common 15000 A 10000 The solution curves phase trajectories) are a closed curves that have the equilibrium point (5000, 200) inside them The solution curves (phase trajectories) are a closed curves that have the equilibrium point (5500, 250) inside them. The solution curves (phase trajectories are all open curves that have the equilibrium point (5500, 250) inside them. The solution curves (phase trajectories) are a open curves that have the equilibrium point (5000, 200) inside them. The solution curves phase trajectories) are a closed curves that have the equilibrium point (5000, 250) inside them.

Explanation / Answer

SOLUTION :-

(d) option 1

Explanation :-

This says that in the beginning there aren’t enough aphids to support 200 ladybugs, so the ladybug population decreases rapidly, while the aphid population increases very slowly. As more ladybugs die, the rate of decrease of the population of ladybugs slows, while the rate of growth of the aphid population increases.

After the ladybug population bottoms out at 100, the ladybug population starts increasing; the aphid population is still growing rapidly, eventually getting to a maximum of almost 15,000 aphids. Of course, with all these aphids to eat, the ladybug population increases rapidly, eventually causing the aphids to start dying o.

The ladybugs reach a maximum population of more than 350, but by this point the falling aphid population means that this is unsustainable. As the aphid population bottoms out at 1000, the ladybug population falls through 200, starting the cycle anew

(e)

Option 5

Both graphs have the same period and the graph of L peaks about a quarter of a cycle after the graph of A.

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