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The number of fish x in a small lake at time t months after a certain instant, is modelled by the DE dx dt = x(1 − kt), where is a positive constant. We may assume that can be treated as a continuous variable. It is estimated that there are 10 000 fish in the lake when t = 0 and 12 months later Ithe number of fish returns back to 10 000.

The number of fish x in a small lake at time t months after a certain instant, is modelled by the DE dx dt = x(1 − kt), where is a positive constant. We may assume that can be treated as a continuous variable. It is estimated that there are 10 000 fish in the lake when t = 0 and 12 months later Ithe number of fish returns back to 10 000.

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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The number of fish x in a small lake at time t months after a certain instant, is modelled by the DE dx dt = x(1 − kt), where is a positive constant. We may assume that X can be treated as a continuous variable. It is estimated that there are 10 000 fish in the lake when t = 0 and 12 months later Ithe number of fish returns back to 10 000.
Transcribed Image Text:The number of fish x in a small lake at time t months after a certain instant, is modelled by the DE dx dt = x(1 − kt), where is a positive constant. We may assume that X can be treated as a continuous variable. It is estimated that there are 10 000 fish in the lake when t = 0 and 12 months later Ithe number of fish returns back to 10 000.
(a) The value of the constant k is your answer to three decimal places.) (Round (b) While studying what will happen to the fish population in the long run, we find that lim x(t) = t→∞ Enter 1000000 for the limit in (b) f you think it is negative infi ty and 1000000 if you think it is positive infinity
Transcribed Image Text:(a) The value of the constant k is your answer to three decimal places.) (Round (b) While studying what will happen to the fish population in the long run, we find that lim x(t) = t→∞ Enter 1000000 for the limit in (b) f you think it is negative infi ty and 1000000 if you think it is positive infinity
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