14. Suppose a population P(t) satisfies a logistic modeldPdtsubject to P(0) = 50.a) What is the carrying capacity?b) What is P'(0)?= 0.4P-0.001P²c) When will the population reach 50% of the carrying capacity?

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Answered: 14. Suppose a population P(t) satisfies…

Calculus: Early Transcendentals

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Chapter1: Functions And Models

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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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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.)
38. Given the power regression model y = 40x^1.3, which is the linear regression model after transforming to a log-log graph? Y = 1.3X + 1.60 Y = 0.20X + 0.11 Y = 0.20X + 0.36 Y = 1.60X + 0.11
Solue this Logistic stchostic differentialeho where a, c constant ッn er Process by using reducible
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?
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An observation indicates that the initial population of grey seals P(t) nearby a harbor is 25 and satisfies the logistic equation P(t)' = 0.0225P(t) - 0.0003P(t)² (with t in months.) a) Apply Euler's method together with any computer program (compulsory) to approximate the solution for 10 years. Use the step size of h = 1 and then with h = 0.5. (LT-C3) b) Find out the percentage of the limiting population of 75 grey seals has been attained after 5 years and after 10 years. (LT-C2) c) Summarize your findings in (b). (LT-C4)

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14. Suppose a population P(t) satisfies a logistic model dP dt = 0.4P-0.001P² subject to P(0) = 50. a) What is the carrying capacity? b) What is P'(0)? c) When will the population reach 50% of the carrying capacity?