Ws 5.5 Partial Fractions And Logistic Growth Word Problem Worksheet Page 5
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10Calculus Maximus
WS 5.5: Partial Fractions & Logistic
Short Answer/Free Response
Work the following on notebook paper.
9. Suppose the population of bears in a national park grows according to the logistic differential equation
dP
2
5
P
0.002
P
, where P is the number of bears at time t in years.
dt
____________. Sketch the graph of
(a) If
P
(0) 100
, then lim ( )
P t
P t . For what values of P
( )
t
is the graph of P increasing? decreasing? Justify your answer.
____________. Sketch the graph of
(b) If
P
(0) 1500
, lim ( )
P t
P t . For what values of P is
( )
t
the graph of P increasing? decreasing? Justify your answer.
____________. Sketch the graph of
(c) If
P
(0)
3000
, lim ( )
P t
P t . For what values of P is
( )
t
the graph of P increasing? decreasing? Justify your answer.
(d) How many bears are in the park when the population of bears is growing the fastest? Justify
your answer.
Page 5 of 10
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