Ws 5.5 Partial Fractions And Logistic Growth Word Problem Worksheet Page 7
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10Calculus Maximus
WS 5.5: Partial Fractions & Logistic
11. (Calculator Permitted) The rate at which a rumor spreads through a high school of 2000 students can
dP
be modeled by the differential equation
0.003 (2000
P
P
)
, where P is the number of students
dt
who have heard the rumor t hours after 9AM.
(a) How many students have heard the rumor when it is spreading the fastest?
, solve for P as a function of t.
(b) If
P
(0)
5
(c) Use your answer to (b) to determine how many hours have passed when the rumor is spreading the
fastest. Give exact and 3-decimal approximation.
(d) Use your answer to (b) to determine the number of people who have heard the rumor after two hours.
Give exact and 3-decimal approximation.
Page 7 of 10
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