Suppose That a Population Grows According to a Logistic Model

question 135

Essay

Suppose that a population grows according to a logistic model.(a) Write the differential equation for this situation with k = 0.01 and carrying capacity of 60 thousand.(b) Solve the differential equation in part (a) with the initial condition t = 0 (hours) and population P = 1 thousand.(c) Find the population for t = 10 hours, t = 100 hours, and t = 1000 hours.(d) After how many hours does the population reach 2 thousand? 30 thousand? 55 thousand?
(e) As the time t increases without bound, what happens to the population?
(f) Sketch the graph of the solution of the differential equation.

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Definitions:

Kindreds

A network of relatives within which individuals possess rights and obligations; often extending beyond immediate family.

Focal Person

An individual who is the center of attention or the main subject of study in a particular research or discussion.

Kindreds

Networks of relatives extended beyond the immediate family, including all individuals related by blood, marriage, or adoption.

EGO

In kinship terminology, the central person from whom the degree of each relationship is traced.