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Calculus
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9 Jun 2020

Self cleaning property of lake is given as,

‘k’ is the amount of effluent added to the lake (k>1). What is the maximum value ‘k’ possible for the lake to clean itself and remain stable?

 

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Calculus 2
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Analyze phase planes
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24 Jul 2020

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Related questions


I just need help with 32 and part a only. Thank you!

The local pond is filled with phytoplankton with squids as their natural predators to maintain the population growth of phytoplankton. The Lotka-Volterra equation describes predator prey relationship as:

 

Phytoplankton :

 

Squids :

The rate of population growth of phytoplankton and squids is given by above equation with ‘a’ is the growth rate of phytoplankton and ‘b’ is predation rate. Factor ‘c’ represents the mortality rate of squids and ‘d’ as growth rate of squids with predation.

Industrial effluent is being discharged into the lake and is toxic to both species, but directly consumed by phytoplankton only. If squids start consuming toxic borne plankton, the population growth rate will change. What pair of modified equations describe this scenario? Consider ‘x’ as toxicity rate common to both species.

 

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