dN Assume that N(t) denotes the size of a population at time t, and that in some conditions N(t) satisfies the differential equation = rN, where r is a constant. (a) Find the per capita growth rate. (b) Assume that r< 0 and that N(0) = 20. Is the population size at time 1 greater than 20 or less than 20? Explain your answer. (a) The per capita growth rate is dN (b) The population is changing at a rate of = rN. Since N is and r is the product is Therefore the function N(t) must be Thus the population at t= 1 will be 20.

dN Assume that N(t) denotes the size of a population at time t, and that in some conditions N(t) satisfies the differential equation = rN, where r is a constant. (a) Find the per capita growth rate. (b) Assume that r< 0 and that N(0) = 20. Is the population size at time 1 greater than 20 or less than 20? Explain your answer. (a) The per capita growth rate is dN (b) The population is changing at a rate of = rN. Since N is and r is the product is Therefore the function N(t) must be Thus the population at t= 1 will be 20.

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Description: 1-5)First three drop box options (zero, negative, positive)Fourth box options (increase, decrease, constant)Last box ( ) Assume that N(t) denotes the size of a population at time t, and that in some conditions N(t) satisfies the differential equati

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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Question

1-5)

First three drop box options (zero, negative, positive)

Fourth box options (increase, decrease, constant)

Last box (<,>)

Assume that N(t) denotes the size of a population at time t, and that in some conditions N(t) satisfies the differential equation = rN, wherer is a constant.
NP
(a) Find the per capita growth rate.
(b) Assume that r< 0 and that N(0) = 20. Is the population size at time 1 greater than 20 or less than 20? Explain your answer.
(a) The per capita growth rate is
(b) The population is changing at a rate of -
dN
= rN. Since N is
the product is
Therefore the function N(t) must be
and r is
dt
Thus the population at t= 1 will be
20.

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