Ws 5.5 Partial Fractions And Logistic Growth Word Problem Worksheet Page 3
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10Calculus Maximus
WS 5.5: Partial Fractions & Logistic
dP
P
5. The population
P t of a species satisfies the logistic differential equation
, where
( )
P
2
dt
5000
the initial population is
P
(0)
3000
and t is the time in years. What is lim ( )
P t
?
t
(A) 2500
(B) 3000
(C) 4200
(D) 5000
(E) 10,000
dP
2
6. Suppose a population of wolves grows according to the logistic differential equation
,
3
P
0.01
P
dt
where P is the number of wolves at time t, in years. Which of the following statements are true?
I. lim ( ) 300
P t
t
P
II. The growth rate of the wolf population is greatest when
150
.
P
III. If
300
, the population of wolves is increasing.
(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) I, II, and III
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