(adsbygoogle = window.adsbygoogle || []).push({}); The initial mass of a species of fish in a lake is 7 million tonnes. The mass of fish, if left alone, would increase at a rate proportional to the mass, with a proportionality constant of 2/year. However, commercial fishing removes fish mass at a constant rate of 15 million tonnes per year. Answer the following questions.

(a) When will all the fish be gone?

(b) What should the fishing rate be so that the mass of fish remains constant?

I am confused as to how to start this question. i am unsure whether i am suppose to use dp/dt = ap-bp^2 nor do i know how to plug everything in. In class, i was given that p(t) = ap0/[bp0 + (a-bp0)e^(-a(t-t0))], i just do not know how to use it.

This is my attempt, I just do not know how to start. but I am guessing for (a) that i would have to set somethign = to zero. I am given a = 2, P(0) = 7000000? and b=15?? But I am confused because if i set p(t)=0, then 0=ap0, and both a and p0 are given.... so i KNOW i am doing somethign wrong but do not know how to fix it.

I just have some new insight on problem (a), perhaps i do not need to use the complicated model but just the easy P=P0e^a(t-t0) where a = 2-15, and p0 is 7mill and t0 is 0.. this makes a lot of sense to me. but then it is insolvable since i end up gett 0=e^-13t so once again i am back to square 1 and confused.

and i am still confused as to how to start (b) , any help would be greatly appreciated as i have no idea what to do .

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# Differential equations - population growth models

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