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The population of lemmings L(t) at the top of a cliff is increasing with the formula L(t) = 1000e0.05Ł However, lemmings leap off the cliff at a rate equal to 0.1L and pile up at the bottom. (a) Write a pure-time differential equation for the umber of lemmings B(t) piled up at the bottom of the cliff. (b) Solve the differential equation using initial condition B(0) = 0. B(t) as t approaches infinity. L(t) (c) Find the limit of the ratio

The population of lemmings L(t) at the top of a cliff is increasing with the formula L(t) = 1000e0.05Ł However, lemmings leap off the cliff at a rate equal to 0.1L and pile up at the bottom. (a) Write a pure-time differential equation for the umber of lemmings B(t) piled up at the bottom of the cliff. (b) Solve the differential equation using initial condition B(0) = 0. B(t) as t approaches infinity. L(t) (c) Find the limit of the ratio

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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The population of lemmings L(t) at the top of a cliff is increasing with the formula L(t) = 1000e0.05t However, lemmings leap off the cliff at a rate equal to 0.1L and pile up at the bottom. (a) Write a pure-time differential equation for the number of lemmings B(t) piled up at the bottom of the cliff. (b) Solve the differential equation using initial condition B(0) = 0. B(t) as t approaches infinity. L(t) (c) Find the limit of the ratio
Transcribed Image Text:The population of lemmings L(t) at the top of a cliff is increasing with the formula L(t) = 1000e0.05t However, lemmings leap off the cliff at a rate equal to 0.1L and pile up at the bottom. (a) Write a pure-time differential equation for the number of lemmings B(t) piled up at the bottom of the cliff. (b) Solve the differential equation using initial condition B(0) = 0. B(t) as t approaches infinity. L(t) (c) Find the limit of the ratio
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