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Assume that a population, P, is changing at a rate inversely proportional to 50 + P. Does it make sense to use differential equations to model the population size? If so, write the differential equation. If not, explain why. O No, P = kt is a simple relationship and there is no rate of change so no need to use differential equations. dP O Yes, = k(50+ P) is a differential equation with a rate of change. dt O Yes, dP dt O No, P = = k 50+P is a differential equation with a rate of change. k is a simple relationship and there is no rate of change so no need to use differential equations. t

Assume that a population, P, is changing at a rate inversely proportional to 50 + P. Does it make sense to use differential equations to model the population size? If so, write the differential equation. If not, explain why. O No, P = kt is a simple relationship and there is no rate of change so no need to use differential equations. dP O Yes, = k(50+ P) is a differential equation with a rate of change. dt O Yes, dP dt O No, P = = k 50+P is a differential equation with a rate of change. k is a simple relationship and there is no rate of change so no need to use differential equations. 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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Assume that a population, P, is changing at a rate inversely proportional to 50 + P. Does it make sense to use differential equations to model the population size? If so, write the differential equation. If not, explain why. No, P = kt is a simple relationship and there is no rate of change so no need to use differential equations. dP Yes, = k(50 + P) is a differential equation with a rate of change. dt Yes, No, dP dt P = k 50+P is a differential equation with a rate of change. k is a simple relationship and there is no rate of change so no need to use differential equations. t
Transcribed Image Text:Assume that a population, P, is changing at a rate inversely proportional to 50 + P. Does it make sense to use differential equations to model the population size? If so, write the differential equation. If not, explain why. No, P = kt is a simple relationship and there is no rate of change so no need to use differential equations. dP Yes, = k(50 + P) is a differential equation with a rate of change. dt Yes, No, dP dt P = k 50+P is a differential equation with a rate of change. k is a simple relationship and there is no rate of change so no need to use differential equations. t
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