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

See similar textbooks

Similar questions

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
12. Express the following equations in logarithmic form. (a) 10 = 1000 (b) Qt = (c) e2 = 7.3891 (d) 83 = 2 (e) pk = 3 (f) 5-3 = 1 125
The population of an aquatic species in a certain body of water is approximated by the logistic function 37,500 where t is measured in years. Find G(t) = = ,-0.56t' the population and its growth rate at the following times. a. 1 year b. 5 years c. 12 years d. What happens to the rate of growth over time? 1 + 12e The population in 1 year is 4774 . (Round to the nearest whole number.) The population in 5 years is 21680. (Round to the nearest whole number.) The population in 12 years is 36965. (Round to the nearest whole number.) The growth rate in 1 year is per year. (Round to the nearest whole number.)
A study of Maryland's portion of Chesapeake Bay found the following information about stocks of market-sized oysters.† In 1994, the stocks were 218 million. (This is the number you will use for the initial population N(0).) The carrying capacity is 5089 million oysters. The intrinsic exponential growth rate is 0.274 per year. (a) Find a logistic model N(t) for the number, in millions, of market-sized oysters. Take t to be the time in years since 1994. (Rround all regression parameters to three decimal places.) N(t) = (b) Plot the graph of the model you found in part (a) over the first 20 years. (c) How many market-sized oysters does your model predict for 2007? Round your answer, in millions, to the nearest whole number. million oysters (d) The actual number of market-sized oysters was found to be 82 million. Use the Internet to find possible explanations for the reduced levels of oysters in Chesapeake Bay.
The population, P, of kangaroos in a reservation is modelled by the logistic dP equation = dt 2P (5- reservation. - P 10 000 ) where t is measured in days. It is estimated that initially the population of the kangaroos is 15% of the carrying capacity of the (i) What is the initial population of the kangaroos? (ii) What is the population of the kangaroos when the rate of increase is a maximum?
Assume there is a certain population of fish in a pond whose growth is described by the logistic equation. It is estimated that the carrying capacity for the pond is 2000 fish. Absent constraints, the population would grow by 190% per year.If the starting population is given by �0=500, then after one breeding season the population of the pond is given by�1 = After two breeding seasons the population of the pond is given by�2 =
Assume there is a certain population of fish in a pond whose growth is described by the logistic equation. It is estimated that the carrying capacity for the pond is 1200 fish. Absent constraints, the population would grow by 110% per year.If the starting population is given by �0=500, then after one breeding season the population of the pond is given by�1 = After two breeding seasons the population of the pond is given by�2 =
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
Please determine the TIME at which the height of the sunflower is increasing most rapidly and the actual HEIGHT of the sunflower at that time. Differential Equations

Recommended textbooks for you

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Mathematics For Machine Technology

Advanced Math

ISBN:

9781337798310

Author:

Peterson, John.

Publisher:

Cengage Learning,

Basic Technical Mathematics

Advanced Math

ISBN:

9780134437705

Author:

Washington

Publisher:

PEARSON

Topology

Advanced Math

ISBN:

9780134689517

Author:

Munkres, James R.

Publisher:

Pearson,

SEE MORE TEXTBOOKS