Question

A model for the number of people N in a college community who have heard a rumor is given by the equation: N=P(1-e^-.15d) where P is the total population of the community and d is the number of days elapsed since the rumor began. If the number of students is 1,000 find the number of days when 450 students would have heard the rumor?

Answer #1

The number, NN, of people who have heard a rumor spread by mass
media by time tt is modeled by N(t)=a(1−e^(−bt)). There are 100,000
people in the population who hear the rumor eventually. If 30% of
them heard it the first day, find bb, assuming tt is measured in
days. Give your answer to three decimal places.

The number of people in a community who are exposed to a
political announcement can be described by the logistic equation
dN/dt= N(a-bN) (, where a and b are positive constants).
Initially N (0) = 50, and it is observed that N (3) = 200. Find N
(t), N (6) and plot the graph of N (t) if it is known that the
limit amount of people who will see the Ad is 3,000 people.

The number P(t) of people in a community who are exposed to a
particular advertisement is governed by the logistic equation.
initially, P(0) = 200, and it is observed that P(2) = 1500. Solve
for P(t) if it is predicted that the limiting number of people in
the community who will see the advertisement is 35,000. Also, use a
graphing utility to plot the solution curve.

The number P(t) of people in a community who are exposed to a
particular advertisement is governed by the logistic equation.
initially, P(0) = 200, and it is observed that P(2) = 1500. Solve
for P(t) if it is predicted that the limiting number of people in
the community who will see the advertisement is 35,000. Also, use a
graphing utility to plot the solution curve.

Do college students who have volunteered for community service
work differ from those who have not? A study obtained data from 57
students who had done service work and 18 who had not.
Group
Condition
N
X bar
S
1
Service
57
104.12
14.60
2
No Service
18
97.82
14.20
Is there strong evidence (a=0.05 significance level) that
students who have engaged in community service are on the average
more attached to their friends. Please show all working.

Rosy is really getting tired of the loud group behind her in
BioCalculus class, so she decides to spread a rumor about them to
her closest friends. Rosy is very popular and has many friends. The
number of friends of Rosy, , who have heard the rumor by time in
hours since the rumor started to spread can be approximated by a
function of the form
N ( t) = L / 1 + C e^- k t If you are...

Suppose that t weeks after the start of an epidemic in a certain
community, the number P(t) of people who have caught the disease is
given by the logistic curve P(t) = 1500 5 + 295 e-0.9t (a) How many
people had the disease when the epidemic began? (b) Approximately
how many people in total will get the disease? (c) When was the
disease spreading most rapidly? (d) How fast was the disease
spreading at the peak of the epidemic?...

The random
variable x
is the number
of people who have a college degree in a randomly selected group of
four adults from a particular town. Its probability distribution is
given in the table. Find the mean
and variance of the
random
variable x.
X
0
1
2
3
4
p(x)
0.13
0.34
0.25
0.16
0.12

There are 1,000 students in a college dormitory, and some
students have been diagnosed with meningitis, a highly contagious
disease. A model for how many students will have the disease after
n days is
m[n + 1] = m[n] + 0.00090*m[n]*(1000 - m[n]);
m[n + 1] = m[n] + 0.00090 m[n] (1000 - m[n])
Two students returned from spring break with meningitis.
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versus the number of days that have...

Throughout the country, the proportion of first-time, first-year
community college students who return for their second year of
studies is p = 0.52 according to the Community College Survey of
Student Engagement. Suppose a community college institutes new
policies geared toward increasing student retention. The first year
this policy was in place there were n = 2843 first-time, first-year
students (N = 1, 050,000). Of these students, x = 1516 returned for
their second year of studies. Treat these students...

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