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.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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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.
Transcribed Image Text: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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