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Suppose that a certain population obeys the logistic equation dy = Ty dt K a) If yo K find the time 7 at which the initial population has doubled. Find the value of r corresponding to r = 0.021 per year. NOTE: Enter an exact answer. T = = a, find the time T at which K v(T') = B, where 0 < a, ß < 1. K b) If Y0 Observe that T → 0 as a → 0 or as 3→ 1. Find the value of T for r = 0.021 per year, a = and 8 = 0.8. 9' NOTE: Enter an eroct answer.

Suppose that a certain population obeys the logistic equation dy = Ty dt K a) If yo K find the time 7 at which the initial population has doubled. Find the value of r corresponding to r = 0.021 per year. NOTE: Enter an exact answer. T = = a, find the time T at which K v(T') = B, where 0 < a, ß < 1. K b) If Y0 Observe that T → 0 as a → 0 or as 3→ 1. Find the value of T for r = 0.021 per year, a = and 8 = 0.8. 9' NOTE: Enter an eroct answer.

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 di = ru(1 -2). K a) If yo = find the time r at which the initial population has 9 doubled. Find the value of T corresponding to r = 0.021 per year. NOTE: Enter an ezact answer. b) If Y0 = a, find the time T at which K v(T) =B, where 0 < a, B < 1. K Observe that T → o as a → 0 or as 3 1. Find the value of T for r = 0.021 per year, a = and B = 0.8. 9' NOTE: Enter an exoct answer. T =
Transcribed Image Text:Suppose that a certain population obeys the logistic equation di = ru(1 -2). K a) If yo = find the time r at which the initial population has 9 doubled. Find the value of T corresponding to r = 0.021 per year. NOTE: Enter an ezact answer. b) If Y0 = a, find the time T at which K v(T) =B, where 0 < a, B < 1. K Observe that T → o as a → 0 or as 3 1. Find the value of T for r = 0.021 per year, a = and B = 0.8. 9' NOTE: Enter an exoct answer. T =
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