Algebra Exercises ( 2 questions)

Please Respond only to exercises 39 and 41. ( see attachment). Be sure to show work or an explanation with your solution; generally speaking, do not just state your answer.
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488
ExpoNpmrrAl AND Locamrsurc FuxcrroNs
38. According to ohioBiz, the census data for Lake County. ohio is as follows:
Year f
Popuiation
1860
15576
t
1960
14870A
Year
Population
i870
i880
t6326
15935
1890
1900
21680
r8235
L970
1980
1990
197200
272801
215499
(u) Use your calculator
1920
28667
1910
22927
1930
1940
1950
41674
50020
75979
2000
227511
to fit a logistic model to these data, using
r:
yea^r 1860.
0 to represent the
(b) Graph these data and your logistic function on your calculator to judge the reasonableness of the fit.
(c) Use this model to estimate the population of Lake County in 2010. (The 2010
gave the population to be 230,041.)
(d) According to your model, what is the population limit of Lake county, ohio?
census
$ccording to facebook, the number of active users of facebook has grovra sigrrificantly since
its iuitial launch from a Harvard dorm room in February 2004. The chart below has the
approximate number U(r) of active users, in million$, r months after February 2004. For
example, the first entry (10, 1) rneans that there were 1 million active users in December 2004
and the last entry (77,500) means that there were 500 million active users in July 2010.
Month r
Active Users in
Millions t/(r)
10
22
34
38
44
54
59
60
62
65
67
70
72
1
5.5
L2
20
50
100
150
175
200
250
300
350
400
tt
500
With the help of your classmates, find a model for this data.
40. Each Monday during the registration period before the Fall Semester at LCCC, the Enrollment
Planning C-ouncil gets a report prepared by the data analysts in Institutional Effectiveness
and
Planning-23 While the ongoing enrollment data is analyzed in many different ways, we shall
focus only on the overall headcount. Below is a chart of the enrollment data for Fall Semester
2008′ It starts 21 weeks before “opening Day” and ends on *Day 15,, of the semester, but
we have relabeled the top row to be s : 1 through r :24 so that the math is easier. (Thus,
r : 22 is Opening Day.)
Week z
1
2
3
4
5
r,
7
B
1194
1564
20a1
2475
2842
3141
3527
37S0
I
10
11
t2
13
t4
15
16
4065
4371
4671
4945
5300
5657
6056
6478
Total
Headcou-nt
Week
r
Total
Headcount
xThe authors thank Dr.
Wendy Marley and her sta$ for this data and Dr. Marcia Ballinger for the permission to
use it in this problem.
6.5 ApplrcATroNs op ExpoNpNTrAL ,qruo Loc,R.nrrnMrc FuNcrroNs
Week
r
489
L7
18
19
20
2L
22
23
24
7167
7772
8505
9256
10201
10743
L1102
11181
TotaI
Headcount
With the help of your classmates, find a model for this data. Unlike most of the phenomena
we have studied in this section, there is no singie differential equation which governs the
enrollment growth. Thus there is no scientific reason to rely on a logistic function even
though the data plot may lead us to that model. What are some factors whieh influence
enrollment at a community college and how can you take those into account mathematically?
n we wrote this exercise, the Enrollment Planning Report for Fall Semester 2009 had
only 10 data points for the first 10 weeks of the registration period. Those numbers are given
below.
Week
r
1
2
1380
2000
t.,
4
5
6
7
8
I
10
2639
3153
3499
3831
4283
4742
5L23
5398
I
Total
Headcount
With the help of your classmates, find a model for this data and make a prediction for the
Opening Day enrollment as well as the Day 15 enrollment. (WARNING: The registration
period for 2009 was one week shorter than it was in 2008 so Opening Day would be r :21
and Day 15 is
r:23.)

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