A population is modeled by a function P that satisfies the logistic differential equation dP di (a) If P(0)=3, what is lim P(r)? If P(0)-20, what is lim P()? fam (b) If P(0)-3, for what value of P is the population growing the fastest? (c) A different population is modeled by a function Y that satisfies the separable differential equatice dy Find Y() if (0)-3. (d) For the function Y found in part (c), what is lim Y()? 1-940

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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A population is modeled by a function P that satisfies the logistic differential equation
dP
#-5 (¹-6)
di
(a) If P(0)=3, what is lim P(r)?
If P(0)-20, what is lim P()?
fam
(b) If P(0)-3, for what value of P is the population growing the fastest?
(c) A different population is modeled by a function Y that satisfies the separable differential equatice
dy
2-3 (1-2)
Find Y() if (0)-3.
(d) For the function Y found in part (c), what is lim Y()7
199
Transcribed Image Text:A population is modeled by a function P that satisfies the logistic differential equation dP #-5 (¹-6) di (a) If P(0)=3, what is lim P(r)? If P(0)-20, what is lim P()? fam (b) If P(0)-3, for what value of P is the population growing the fastest? (c) A different population is modeled by a function Y that satisfies the separable differential equatice dy 2-3 (1-2) Find Y() if (0)-3. (d) For the function Y found in part (c), what is lim Y()7 199
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