The Pacific halibut fishery has been modeled by the differential equation dy ky 1 dt M where y(t) is the biomass (the total mass of the members of the population) in kilograms at timet (measured in years), the carrying capacity is estimated to be M = 9 × 107 kg, and k = 0.79 per year. (a) If y(0) = 2 x 107 kg, find the biomass a year later. (Round your answer to two decimal places.) x 107 kg (b) How long will it take for the biomass to reach 4 x 107 kg? (Round your answer to two decimal places.) yr

The Pacific halibut fishery has been modeled by the differential equation dy ky 1 dt M where y(t) is the biomass (the total mass of the members of the population) in kilograms at timet (measured in years), the carrying capacity is estimated to be M = 9 × 107 kg, and k = 0.79 per year. (a) If y(0) = 2 x 107 kg, find the biomass a year later. (Round your answer to two decimal places.) x 107 kg (b) How long will it take for the biomass to reach 4 x 107 kg? (Round your answer to two decimal places.) yr

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

The Pacific halibut fishery has been modeled by the differential equation
dy
ky 1
dt
M
where y(t) is the biomass (the total mass of the members of the population) in kilograms at timet (measured in years), the carrying capacity is estimated to be M = 9 × 107 kg, and k = 0.79 per year.
(a) If y(0)
= 2 x 107 kg, find the biomass a year later. (Round your answer to two decimal places.)
x 107 kg
(b) How long will it take for the biomass to reach 4 x 107 kg? (Round your answer to two decimal places.)
yr

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