Question

Consider the folowing table Mote: This exercise correspornds bo the subiection Mbcel Choces.) production, Given the Amount Invested In Capital Capital x Creilion dollars) (billion units) (a) Describe Oie behavor tuggested by "cat ter plot of the data aglist the types of red h that ehbe-t behm 24. The scatter pot i concave -ee "he left of..2. and coreave ee the right af" . 24 Thn behavor tu ν' function ses and ist the Evpes of Descibe the possible end behvior as input O Production should approach 0 as capital ependture increases. A logistic model wouidti ity O Production shold contnue to increase to a imiting value as capital expendune increaestdt the Productor, should contrue to ncrease wrout bound as caota-apenditure increases. ㅅ cube, quadrate, korthree, e:ponential model void fe this potibaty. s invested in captal, wth data from 6 5xs44. ounallmercal values to four decinal places.) (a) wnte the function of the model that best exhibits the end behavior of the data of the production level in bilon units, wthere x mo ars a nvasted in capita, with data hon 6 s*s8 ond at nuarca values to fou 0.002-0.1612+4.637x-4473 x 6 Abot eh. intrx.coa ^ 目Aber henstru.dea ^ @ noble,Jung..apo ^ 匎Abon. div.deo ^ ^ O Type here to search

Answer 1

a) Describe the behavior suggested by a scatter plot of the data and list the data and list the types of model that exhibits the behavior. A scatter plot of the data is increasing and appears to have an inflection point near x-24. The scatter plot is concave to the left ofxz24 and concave to the right of x-24 million Production P dollars billion units Capital x Production P 80 18 70 10 39 60 43 24 50 30 46 61 42 30 48 78 20 10 30

Production P 90 0.0116x2 + 0.5273x + 22.48 70 50 400 30 20 10 100 30 400 50 P()-0.0116x*2+0.5279x+22.8 Production P 90 80 0.0033x3-0.2603x, 6.678x-10.216 y 0.0116x2+0.5279x 22.48 y # 70 50 400 30 10 10 20 30 4i 50 60 P(x)-0.0033 3-0.2603x 2+6.678x-10.216

Production P 90 80 y- 21.183e 0 0255 70 60 50 40 30 20 100 0 0 10 20 30 440 50 P(x)-21.183exp(0.0268x) (exponential curve) From the graph it looks a cubic curve fits the curve in a better manner. So the answer is P(x)-0.0033 3-0.2603x*2+6.678x-10.216

production level Excel CHART TOOLS HOME INSERT PAGE LAYOUT FORMULAS DATA REVIEW VIEW DESIGN FORMAT Add Chart Quick Element-Layout- dh Ayes Change Switch Row/ SelectMove ColumnDat Chart Type Chart Colors ▼ Chart Styles Type Location h Axis Titles Chart Title Data Labels» Data Table Production P million dollarslbillion units b Error Bars* Capital x Production P Gridlines 18 10 Legend 43 nd Lines Irendline 42 61 Up/Down Bars 12 13 14 20 Linear Eorecast 15 17 Moving Average 18 More Trendline Options.. Sheet Sheet3 Sheet2 READY闘 AVERAGE 37.08333333 COUNT: 14 SUM: 445

production level- Excel CHART TOOLS FILE HOME INSERT PAGE LAYOUT FORMULAS DATA REVIEW VIEW DESIGN FORMAT Sign in Add Chart Quick Change Element Layout Colors Switch Row SelectChange Move Column Data Chart Type Chart Chart Layouts Chart Styles Type Location Format Trendline Production P million dollars billion units TRENDLINE OPTIONS ▼ Production P y-0.0033k0.2603+6.678x-10.216 0 50 Order 3 Polynomial 20 Poyer Moving Average Period 2 12 Trendline Name 14 50 Poly. (Production P) Automatic o custom 16 17 To get the cubic equation in Excel we use the Trendline concept in EXCEL and obtain the desired values or the cubic equation 18 0.0 0.0 periods Set Intercept 0.0 Display Equation on chart Display R-squared value on chart Sheet1 Sheet3 Sheet2