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Suppose that a certain population satisfies the initial value problem dy dt 1+ sint = r(t)y – k, y(0) = Y0, where the growth rate r(t) is given by %3D r(t): and k represents the rate of predation. 1 a) Suppose that k = Select the figure that represents y versus t for y = 0.5,0.75, 1. Figure 4 b) Estimate the critical initial population y, below which the population will become extinct. NOTE: Round your answer to two decimal places. Ye =0.6 c) Find a general relation between k and the corresponding y then plot y. versus k. There is a linearv dependence of y, on k.

Suppose that a certain population satisfies the initial value problem dy dt 1+ sint = r(t)y – k, y(0) = Y0, where the growth rate r(t) is given by %3D r(t): and k represents the rate of predation. 1 a) Suppose that k = Select the figure that represents y versus t for y = 0.5,0.75, 1. Figure 4 b) Estimate the critical initial population y, below which the population will become extinct. NOTE: Round your answer to two decimal places. Ye =0.6 c) Find a general relation between k and the corresponding y then plot y. versus k. There is a linearv dependence of y, on k.

Advanced Engineering Mathematics
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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Suppose that a certain population satisfies the initial value problem dy r(t)y - k, y(0) = yo, where the growth rate r(t) is given by dt 1+ sin t r(t) and k represents the rate of predation. %3D 3D a) Suppose that k = 1 Select the figure that represents y versus t for yo = 0.5, 0.75, 1. Figure 4 b) Estimate the critical initial population y, below which the population will become extinct. NOTE: Round your ansuer to tuo decimal places. 3D Ve =0.6 c) Find a general relation between k and the corresponding yes then plot y. versus k. There is a linear dependence of y. on k.
Transcribed Image Text:Suppose that a certain population satisfies the initial value problem dy r(t)y - k, y(0) = yo, where the growth rate r(t) is given by dt 1+ sin t r(t) and k represents the rate of predation. %3D 3D a) Suppose that k = 1 Select the figure that represents y versus t for yo = 0.5, 0.75, 1. Figure 4 b) Estimate the critical initial population y, below which the population will become extinct. NOTE: Round your ansuer to tuo decimal places. 3D Ve =0.6 c) Find a general relation between k and the corresponding yes then plot y. versus k. There is a linear dependence of y. on k.
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