The population C of coyotes (a predator) at time t (in months) in a region is estimated to be at 12 and the population R of rabbits (its prey) is estimated to be zt C = 5000 + 2000 sin - R= 25, 000 + 15, 000 cos (1)Use a graphing utility to graph both models in the same viewing window. Use the window setting 0

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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The population C of coyotes (a predator) at time t (in months) in a region is estimated to be
at
C = 5 000 + 2 000 sin
12
and the population R of rabbits (its prey) is estimated to be
at
R = 25, 000 + 15, 000 cos -
12
(1)Use a graphing utility to graph both models in the same viewing window. Use the window setting 0 <t < 100.
(2)Use the graphs of the models in part (1) to explain the oscillations in the size of each population.
(3)The cycles of each population follow a periodic pattern. Find the period of each model and describe several factors that could be contributing to the cyclical
patterns.
Transcribed Image Text:The population C of coyotes (a predator) at time t (in months) in a region is estimated to be at C = 5 000 + 2 000 sin 12 and the population R of rabbits (its prey) is estimated to be at R = 25, 000 + 15, 000 cos - 12 (1)Use a graphing utility to graph both models in the same viewing window. Use the window setting 0 <t < 100. (2)Use the graphs of the models in part (1) to explain the oscillations in the size of each population. (3)The cycles of each population follow a periodic pattern. Find the period of each model and describe several factors that could be contributing to the cyclical patterns.
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