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Survey of Calculus

by: Maxie Champlin

Survey of Calculus MATH 1241

Maxie Champlin
Clayton State
GPA 3.68


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Class Notes
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This 1 page Class Notes was uploaded by Maxie Champlin on Monday October 5, 2015. The Class Notes belongs to MATH 1241 at Clayton State University taught by Staff in Fall. Since its upload, it has received 17 views. For similar materials see /class/219546/math-1241-clayton-state-university in Mathematics (M) at Clayton State University.


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Date Created: 10/05/15
1 The table gives annual sales of at panel TVs with LCD display technology in the United States Europe and Japan for 2001 and 2002 with projections through 2008 Source wwwstrategyanalyticscom Accessed 12203 Year 2001 2002 2003 2004 2005 2006 2007 LCD at panel TV sales million units 2008 068 l 165 l 374 l 565 l 814 1116 1526 l 195439 a Examine the data set and discuss the appropriateness of a linear quadratic cubic eXponential log or logistic model for these data A linear model is not appropriate because rate of change is not constant A cubic or logistic model would be inappropriate because we do not see a noticeable in ection point in the scatter plot The curvature of a logarithmic function does not resemble the data The only two appropriate models are quadratic and eXponential b Determine the most appropriate model Give the equation de ne the variables you use and include units of measure According to the calculated SSE for each model a quadratic function ts the data better than an eXponential function Lx 0267x2 0276x 0184 million units x years after 2000 c Use the result of part b to estimate the sales of at panel TVs with LCD displays in 2010 What must be true for this estimate to be considered reliable Using MathCAD we get that L10 E 2964 million units For a reliable estimate the quadratic pattern of the data must continue for 2 more years 2 The table shows the dividends paid per share of CocaCola stock for selected years between 1987 and 1999 Source Hoover s Online Guide Year 1987 1989 1991 1993 1995 1997 1999 Dividends per share in cents 14172434445664 a On the basis of what you observe in a scatter plot discuss the appropriateness of a linear quadratic cubic eXponential log or logistic model for these data Because the scatter plot indicates an in ection point around 1990 the only functions to consider are cubic and logistic b Determine the most appropriate model Give the equation de ne the variables you use and include units of measure There is no evidence of horizontal asymptotes and the SSE of the logistic function is larger so a cubic function is the most appropriate Dt 70031315 0711312 01429t 140476 cents per share where tis the number ofyears after 1987 c Predict the dividend paid per share for this stock in 1998 and in 2009 Which of these predictions is more reliable and why Using MathCAD to assist with calculations we nd that in 1998 D11 Z 60 cents per share and in 2009 D22 Z 28 cents per share The 1998 prediction is an interpolation and should be fairly reliable However the 2009 prediction should not be considered valid because it is too far outside the data interval


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