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(a) Suppose you're trying to model a population of bunnies. Ini- tially there are 100 rabbits, and you notice that the initial growth rate is 0.08 bunnies/day. Moreover, due to limiting re- sources, it seems that the bunny population doesn't exceed 1000 rabbits. Set up a differential equations model for the number of rabbits and follow the steps from lecture to solve it. You can skip the partial fractions part if you wish. (b) What is the limit of the solution in (a) as t → ∞ ?

(a) Suppose you're trying to model a population of bunnies. Ini- tially there are 100 rabbits, and you notice that the initial growth rate is 0.08 bunnies/day. Moreover, due to limiting re- sources, it seems that the bunny population doesn't exceed 1000 rabbits. Set up a differential equations model for the number of rabbits and follow the steps from lecture to solve it. You can skip the partial fractions part if you wish. (b) What is the limit of the solution in (a) as t → ∞ ?

Advanced Engineering Mathematics
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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(a) Suppose you're trying to model a population of bunnies. Ini- tially there are 100 rabbits, and you notice that the initial growth rate is 0.08 bunnies/day. Moreover, due to limiting re- sources, it seems that the bunny population doesn't exceed 1000 rabbits. Set up a differential equations model for the number of rabbits and follow the steps from lecture to solve it. You can skip the partial fractions part if you wish. (b) What is the limit of the solution in (a) as t → ∞ ?
Transcribed Image Text:(a) Suppose you're trying to model a population of bunnies. Ini- tially there are 100 rabbits, and you notice that the initial growth rate is 0.08 bunnies/day. Moreover, due to limiting re- sources, it seems that the bunny population doesn't exceed 1000 rabbits. Set up a differential equations model for the number of rabbits and follow the steps from lecture to solve it. You can skip the partial fractions part if you wish. (b) What is the limit of the solution in (a) as t → ∞ ?
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