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Marrrta [24]
3 years ago
10

The fish population in a pond evolves according to the logistic equation and a percentage of fish are removed for each unitof ti

me. The situation is modeled by:
dN/dt=rN(1−N/K)−hN

Suppose that the carrying capacity is 900 fish, the intrinsic growth rate is equal to 2, and the harvest rate is 20%.

a. Use the graphical or eigenvalue approach to find and determine the equilibria and their stability.
b. Sketch the solution curves for No=700 and No=1100. (You must label your horizontal and vertical axis)
Mathematics
1 answer:
musickatia [10]3 years ago
8 0

Step-by-step explanation:

Suppose that the carrying capacity is 900 fish, the intrinsic growth rate is equal to 2, and the harvest rate is 20%.

a. Use the graphical or eigenvalue approach

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posledela
We can calculate using cosinus method in triangle
c² = a² + b² - 2ab cos c

Plug in the number to the formula
c² = a² + b² - 2ab cos c
c² = 10² + 8² - 2(10)(8) cos 105°
c² = 100 + 64 - 160 cos 105°
c² = 164 - 160 (-0.26)
c² = 164 + 41.6
c² = 205.6
c = √205.6
c =14.34

C is 14.34 unit length
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