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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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