Question 4Suppose that the differential equationdydE = y(40-y) - 300models & logistic equation with harvesting, where y(t)represents a spotted grunter population in the KnysnaLagoon at time t, mecured in years.Write down the(a) per capita growth rate of the spotted grunterpopulation(b) carrying capacity of the Lagoon.(o rate at which the spotted bagoon grunter areharvested from the Lagoon65

Given: The following differential equation which models a logistic equation with harvesting, where…

Answered: Question 4 Suppose that the…

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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Assume that the population of a town can be modeled by the logistic equation dP/dt = kP(1000 - P). If this town's population was 800 five years ago and is 850 this year, what is its population expected to be five years from now? Round your answer to the nearest integer.
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
At time t = 0, a bacterial culture weighs 2 grams. Three hours later, the culture weighs 5 grams. The maximum weight of the culture is 20 grams. (a) Write a logistic equation that models the weight of the bacterial culture. (Round your coefficients to four decimal places.) 20 y = dy dt = 1 +9e 8 g (c) When will the culture's weight reach 16 grams? (Round your answer to two decimal places.) 9.79 hr (d) Write a logistic differential equation that models the growth rate of the culture's weight. Then repeat part (b) using Euler's Method with a step size of h = 1. (Round your answer to the nearest whole number.) y(5) = 6 -0.3662t = 1.37 0.366y| 1 (1-20) (b) Find the culture's weight after 5 hours. (Round your answer to the nearest whole number.) X g (e) At what time is the culture's weight increasing most rapidly? (Round your answer to two decimal places.) hr
Find the logistic di fferential equation dy -ky 1-
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.)
7. A commercial fishery is estimated to have carrying capacity 40 tons of salmon. Suppose the annual growth rate of total salmon population P (measured in tons) is governed by the logistic equation P' = 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 a constant rate. Then (ii) ( What is the differential equation governing the fish population now? (iii) What is the maximun sustainable harvesting rate? (Justification is required.)
During the period from 1790 to 1930, a country's population P(t) (t in years) grew from 3.7 million to 118.6 million. Throughout this period, P(t) remained close to the solution of the initial value dP problem = 0.03145P-0.0001486P², P(0) = 3.7. dt (a) What 1930 population does this logistic equation predict? (b) What limiting population does it predict? (c) The country's population in 2000 was 350 million. Has this logistic equation continued since 1930 to accurately model the country's population?
During the period from 1790 to 1920, a country's population P(t) (t in years) grew from 3.6 million to 101.6 million. Throughout this period, P(t) remained close to the solution of the initial value problem -0.0001494P² P(0) = 3.6. dP dt = 0.03136P-( (a) What 1920 population does this logistic equation predict? (b) What limiting population does it predict? (c) The country's population in 2000 was 259 million. Has this logistic equation continued since 1920 to accurately model the country's population? (a) The logistic equation predicts the population in 1920 to be million. (Do not round until the final answer. Then round to the nearest thousandth as needed.) K AI C H TU U →> C ¢ ➡ H i O + 2.4 e В → نه Y + - 8 .... : *** 5 Ø Co Less . N 0 .. H A E X U i 9 A C ש Σ VI 8 FR > in X
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

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