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Let P=P(t) denote the population of a rare bird species on the island, where t is the time, in years. Suppose M equals the maximum number of...

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Let P=P(t) denote the population of a rare bird
species on the island, where t is the time, in years.
Suppose M equals the maximum number of
sustainable birds and m equals the minimum
population, below which the species becomes
extinct. The population P can be modeled by the
differential equation. dP—kM PP
E— ( — )( —m) Where k is a positive constant.

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1.Suppose the maximum population M is 1200
birds and the minimum population m is 100
birds. If k=0.001, write the differential equation that
models the population P=P(t). 2.So|ve the differential equation. 3.lf the population at time t=0 is 300 birds, find
the particular solution of the differential
equafion. 4.How many birds will exist in 5 years? 5.Using graphing technology, graph the solution
found in problem 3. 6.The graph from problem 3 seems to have an
inflection point. Approximate the inflection
point from the graph. 7.What conclusions can you draw about the rate
of change ofthe bird population?

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