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
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
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
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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