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uppose that a certain population obeys the logistic equation dy =ry (1-2). dt K If yo find the time 7 at which the initial population has doubled. Find the value of 7 corresponding to r = 0.02 per year. NOTE: Enter the exact answer or approximate your answer to 2 decimal places. T || K 3' = T = -) If = a, find the time T at which Yo K Observe that T→ ∞ as a → ∞ as a → 1 for r = 0.02 per year, a = y(T) K 0 or as 3 → 1. Find the value of T = = ß, where 0

uppose that a certain population obeys the logistic equation dy =ry (1-2). dt K If yo find the time 7 at which the initial population has doubled. Find the value of 7 corresponding to r = 0.02 per year. NOTE: Enter the exact answer or approximate your answer to 2 decimal places. T || K 3' = T = -) If = a, find the time T at which Yo K Observe that T→ ∞ as a → ∞ as a → 1 for r = 0.02 per year, a = y(T) K 0 or as 3 → 1. Find the value of T = = ß, where 0

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 obeys the logistic equation dy = ry(1-2). dt K 3' a) If yo = find the time at which the initial population has doubled. Find the value of 7 corresponding to r = 0.02 per year. NOTE: Enter the exact answer or approximate your answer to 2 decimal places. T Yo y (T) €2008 K K Observe that T → ∞ as a → 0 or as 3 1 b) If = a, find the time T at which for r= 0.02 per year, a = T = = ß, where 0<a, B<1. 1. Find the value of T and 3 = 0.6. 3' NOTE: Enter the exact answer or approximate your answer to 2 decimal places.
Transcribed Image Text:Suppose that a certain population obeys the logistic equation dy = ry(1-2). dt K 3' a) If yo = find the time at which the initial population has doubled. Find the value of 7 corresponding to r = 0.02 per year. NOTE: Enter the exact answer or approximate your answer to 2 decimal places. T Yo y (T) €2008 K K Observe that T → ∞ as a → 0 or as 3 1 b) If = a, find the time T at which for r= 0.02 per year, a = T = = ß, where 0<a, B<1. 1. Find the value of T and 3 = 0.6. 3' NOTE: Enter the exact answer or approximate your answer to 2 decimal places.
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