One class of models for population growth rates in marine fisheries assumes that the harvest from fishing is proportional to the population size. For one such model, we have the the following formula, where G is the growth rate of the population, in millions of tons of fish per year, and n is the population size, in millions of tons of fish. G = 0.4n 1 − n 2 − 0.2n (a) Make a graph of G versus n. Include values of n up to 1 million tons. (b) Use functional notation to express the growth rate if the population size is 0.24 million tons. G Calculate the value. (Round your answer to two decimal places.) million tons per year (c) Calculate G(1.12). (Round your answer to two decimal places.) G(1.12) = million tons per year Explain in practical terms what your answer means. If the population size is 1.12 million tons, then the growth rate is increasing at a rate of 0.03 million tons per year.If the population size is 1.12 million tons, then the population is increasing at a rate of 0.03 million tons per year. If the population size is 1.12 million tons, then the population is decreasing at a rate of 0.03 million tons per year.If the population size is 1.12 million tons, then the growth rate is decreasing at a rate of 0.03 million tons per year. (d) At what population size is the growth rate the largest? (Round your answer to two decimal places.) million tons

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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One class of models for population growth rates in marine fisheries assumes that the harvest from fishing is proportional to the population size. For one such model, we have the the following formula, where G is the growth rate of the population, in millions of tons of fish per year, and n is the population size, in millions of tons of fish.

G = 0.4n

1 −

− 0.2n

(a) Make a graph of G versus n. Include values of n up to 1 million tons.

(b) Use functional notation to express the growth rate if the population size is 0.24 million tons.

Calculate the value. (Round your answer to two decimal places.)
million tons per year

(c) Calculate G(1.12). (Round your answer to two decimal places.)
G(1.12) = million tons per year

Explain in practical terms what your answer means.

If the population size is 1.12 million tons, then the growth rate is increasing at a rate of 0.03 million tons per year.If the population size is 1.12 million tons, then the population is increasing at a rate of 0.03 million tons per year. If the population size is 1.12 million tons, then the population is decreasing at a rate of 0.03 million tons per year.If the population size is 1.12 million tons, then the growth rate is decreasing at a rate of 0.03 million tons per year.

(d) At what population size is the growth rate the largest? (Round your answer to two decimal places.)
million tons

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