Na national park, the population of beavers grows over time At time t=0 where t is measured in years, the population is found to be 20 beavers. EY One zoologist suggests a population model P that satisfies the differential equation dp - (300 - P) Use separation of variables to solve this equation for P (t) with the initial condition P (0) = 20. b) A second zoologist suggests a population model Q that satisfies the logistical differential equation = Q (300 Q) Find the value of 500
Na national park, the population of beavers grows over time At time t=0 where t is measured in years, the population is found to be 20 beavers. EY One zoologist suggests a population model P that satisfies the differential equation dp - (300 - P) Use separation of variables to solve this equation for P (t) with the initial condition P (0) = 20. b) A second zoologist suggests a population model Q that satisfies the logistical differential equation = Q (300 Q) Find the value of 500
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:Ana national park, the population of beavers grows over time. At time t=0 where t is measured in years, the population is found to be 20 beavers.
a) One zoologist suggests a population model P that satisfies the differential equation = (300
P Use separation of variables to solve this
equation for P (t) with the initial condition P (0) = 20.
dQ
b) A second zoologist suggests a population model Q that satisfies the logistical differential equation
dQ
1O (300 - O Find the value of
500
when Q grows most rapidly.
dt
c) For population model Q introduced in part b), use Euler's method using two steps of equal size to appraximate Q) starting at 0 Give your
answer as an integer (whole number) and explain the meaning of your solution. Show the gomputations that lead to your answer
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