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

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

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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

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