Ws 5.5 Partial Fractions And Logistic Growth Word Problem Worksheet Page 8
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10Calculus Maximus
WS 5.5: Partial Fractions & Logistic
dP
2
12. Suppose that a population develops according to the logistic equation
0.05
P
0.0005
P
where t
dt
is measured in weeks.
(a) What is the carrying capacity/limit to growth?
(b) A slope field for this equation is shown below.
I.
Where are the slopes close to zero?
II.
Where are they largest?
III.
Which solutions are increasing?
IV.
Which solutions are decreasing?
(c) Use the slope field to sketch solutions for initial populations of 20, 60, and 120.
I. What do these solutions have in common?
II. How do they differ?
III. Which solutions have inflection points?
IV. At what population level do these inflection points occur?
Page 8 of 10
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