7. A commercial fishery is estimated to have carrying capacity 40 tons of salmon. Supposethe annual growth rate of total salmon population P (measured in tons) is governed by thelogistic equationP' = P(1 – P/40)and initially there are 30 tons of fish.(i)What is the fish population after 1 year? (You may use e 2 2.72.)Suppose that the owner of the fishery decides to harvest h tons of salmon annually at aconstant rate. Then(ii) (What is the differential equation governing the fish population now?(iii)What is the maximun sustainable harvesting rate? (Justification is required.)

Answered: Image /qna-images/answer/d725a096-67f5-4ce6-9df2-2f612ff57deb.jpg

Answered: 7. A commercial fishery is estimated to…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Suppose the population of a species of animals on an island is governed by the logistic model with relative rate of growth k = 0.05 and carrying capacity M= 15000. I.e., the population function P(t) satisfies the equation P' = bP(15000 - P), where b = k/M. If the current population is P(0) = 20000, which one of the following is closest to P(1)? O a) 19700 O b) 19890 Oc) 19680 Od) 19690 Oe) 19805 Of) 19742 Motion
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One of the possible models for the coronavirus is the logistic curve, shown here without scale. This curve shows the total number of cases of people infected with the virus. The rate of change for this curve is the number of ca es per day. 1. On the curve, mark the point at which the number of cases per day is greatest. What is a mathematical term for this point? 2. One of the criteria for re-opening activities is fourteen consecutive da s with a decreasing number of cases. Where is this on the curve? Number of Infected people as a function of time
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