2. In the year 2020 the sea around Australia is teeming with 3-eyed Barrumundi, a genetic mutation of the former freshwater Burrumundi fish which is now extinct. Denote by q(t) the number of tonnes of 3-cyed Barrumundi living in the sea t months after the 1" of January 2020 (1/1/2020). Marine scientists estimate that on 1/1/2020 there were 20,000 tonnes of the fish in the sea (i.e. q(0) = 20, 000). They have also determined that when no fishing of 3-eyed Barrumundi takes place q(t) increases at a rate proportional to the difference between q(t) and an upper limit of 200,000 tonnes. (In answering the following questions, use the value of any constants you derive correct to 4 decimal places.) S (i) Assume that at first there is no fighing of the 3-eyed Barrumundi; people do not like eating fish with three eyes. A survey leads scientists to estimate that there were 22,000 tonnes of the fish in the sea one month after 1/1/2020 If the estimates are correct, how many tonnes of the fish will be in the sea 3 months after 1/1/2020, rounded to the nearest tonne? (ii) The Third Eye Fishing Company starts catching the fish 3 months after 1/1/2020, realising that people do not mind eating the fish in the form of "fish fingers", Assuming the fish is caught at a constant (and continuous) rate of 1000 tonnes per month, work out a revised expression for q(t) for t 2 3. (Hints Simply subtract 1000 from the dq/ dt you used in part (i) to obtain a new da/dt adjusted for exploitation. Use the constant of proportionality calculated in part (i) )