Algebra Exercises ( 2 questions)

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Please Respond only to exercises 39 and 41. ( see attachment).

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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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