Dow Jones Industrial Average The table shows the year-end closing prices p of the Dow Jones Industrial Average (DJIA) from 2000 through 2013, where t is the year, with
0 | 1 | 2 | 3 | |
10,786.85 | 10,021.50 | 8341.63 | 10,453.92 | |
t | 4 | 5 | 6 | 7 |
P | 10,783.01 | 10,717.50 | 12,463.15 | 13,264.82 |
t | 8 | 9 | 10 | 11 |
p | 8776.39 | 10,428.05 | 11,577.51 | 12,217.56 |
t | 12 | 13 | ||
P | 13,104.14 | 16,576.66 |
Spreadsheet at LarsonAppliedCaIculus.com
(a) Determine the average rate of change in the value of the DJIA from 2000 through 2013.
(b) Estimate the instantaneous rate of change in 2005 by finding the average rate of change from 2003 to 2007.
(c) Estimate the instantaneous rate of change in 2005 by finding the average rate of change from 2004 to 2006.
(d) Compare your answers for parts (b) and (c). Which interval do you think produced the best estimate for the instantaneous rate of change in 2005?
Want to see the full answer?
Check out a sample textbook solutionChapter 2 Solutions
Calculus: An Applied Approach (MindTap Course List)
- DVD Player Sales The table shows the number of DVD players sold in a small electronics store in the years 2003-2013. Year DVD players sold 2003 495 2004 513 2005 410 2006 402 2007 520 2008 580 2009 631 2010 719 2011 624 2012 582 2013 635 aWhat was the average rate of change of sales between 2003 and 2013? bWhat was the average rate of change of sales between 2003 and 2004? cWhat was the average rate of change of sales between 2004 and 2005? dBetween which two successive years did DVD player sales increase most quickly? Decrease most quickly?arrow_forwardDVD Player sales The table shows the number of DVD play-ers sold in a small electronics store in the years 2003-2013. What was the average rate of change of sales between 2003 and 2013? Whatwas the average rate of change of sales between 2003 and 2004? What was the average rate of change of sales between 2004 and 2005? Between which two successive years did DVD player sales increase most quickly?arrow_forward6 This table shows the number of subscribers to a video streaming service in the first six years after it was founded. Year 2016 2017 2018 2019 2020 2021 Subscribers 182,000 304,000 433,000 669,000 1,027,000 1,356,000 What was the average rate of change in the number of subscribers between 2017 and 2020?arrow_forward
- Use tables to express and represent the descriptive statistics for thevariables below. Years GDP growth (annual %) Gross capital formation (annual % growth) Labor force participation rate, total (% of total population ages 15-64) (modeled ILO estimate) 2019 0.892 2.556 71.38 2018 1.89 3.862 70.44 2017 0.997 6.158 71.15 2016 1.375 -0.103 70.31 2015 0.921 -6.13 68.74 2014 0.69 3.84 68.39 2013 0.518 5.473 68.53 2012 -0.614 -5.75 67.42 2011 1.73 8.972 67.63 2010 -1.457 -2.039 67.84 2009 -4.345 -18.427 68.15 2008 -0.8117 -8.009 68.46arrow_forwardMaximizing the profit of timber harvesting involves considering all of the following except: A. the interest rate B. the total costs of harvesting C. the ecological value of forest diversity D.the mean annual incrementarrow_forwardWhich of the following is not a good interpretation of a seasonal index of 1.26 for fall quarter sales? O a. Fall quarter sales are 26 perbent higher than the annual average. O b. Fall quarter sales represents 1.26 times the annual average. O c. Fall quarter sales represents an increase of 26 percent over last year's annual average. O d. Fall quarter sales average 126 percent of annual sales.arrow_forward
- HW5 The number of pounds of steam used per month by a chemical plant is thought to be related to the average ambient temperature (in F) for that month. The past year’s usage and temperatures are in the following table: Month Temp. Usage/1000 Month Temp. Usage/1000 Jan. 21 185.79 July. 68 621.55 Feb. 24 214.47 Aug. 74 675.06 Mar. 32 288.03 Sept. 62 562.03 Apr. 47 424.84 Oct. 50 452.93 May 50 454.58 Nov. 41 369.95 June 59 539.03 Dec. 30 273.93 Assuming that a simple linear regression model is appropriate, fit the regression model relating stem usage (y) to the average temperature (x). What is the estimate of ? What is the estimate of expected stem usage when the average temperature is 55 F? What change in mean stem usage is expected when the monthly average temperature changes by 1 F? Suppose that the monthly average temperature is 47 F. Calculate the fitted value of y and the corresponding residual. Test for significance of regression using α=0.01 (Use ANOVA).…arrow_forwardTABLE 1: An economist at Nedbank ran a study of the relationship between FTSE/JSE All Shares index retu (JALSH) and consumer price index (CPI) from 2006 to 2017, the data collected is shown in the Tal below. FTSE/JSE All Shares index return (JALSH) and consumer price index (CPI) from 2006 to 2017. CPI (X) 4.7 7.1 11.5 7.1 4.3 5.0 5.6 5.7 6.1 4.6 6.4 5.3 Year 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Question 1 Use Table 1 above to answer this question JALSH (Y) 0.41 0.19 -0.23 0.32 0.19 0.03 0.27 0.21 0.11 0.05 0.00 0.21 Q.1.1 The estimated regression equation with dependent variable FTSE/JSE All Shares index return (JALSH) and independent variable consumer price index (CPI) was Q.1.1.1 Calculate Bo JALSH, =B₁ + B₂CPI¡arrow_forwardDays $Receipts 14 33.111 28 14.666 42 5.587 56 2.95 70 1.567 84 0.852 98 0.397 112 0.279 126 0.518 Find the average rate of change of the daily receipts from day 42 to day 70.arrow_forward
- . Median Family income has grown substantially in the recent years. Years Income Percent Change Years Income Percent Change 2000 11,500.00 - 2011 17,982.05 2 2001 11,845.00 3 2012 18,341.69 2 2002 12,437.25 5 2013 18,525.10 1 2003 12,934.74 4 2014 19,080.86 3 2004 14,228.21 10 2015 19,844.09 4 2005 15,366.47 8 2016 21,630.06 9 2006 16,288.46 6 2017 22,711.56 5 2007 16,777.11…arrow_forwardIf it cost $8 to fill a gas tank in 1980, how much would it have cost to fill the same tank in 1990? Average Gasoline Prices (per gallon) Price as a Percentage Price Index (1980 = 100) 25.4 Year Price of 1980 Price 1960 $0.31 25.4% 1970 $0.36 $1.22 $1.23 $1.56 $2.84 29.5% 29.5 1980 1990 100.0% 100.0 100.8% 100 8 127.9 2000 2010 127.9% 232.8% 232.8 It would have cost $ in 1990. (Round to the nearest cent as needed.)arrow_forwardLimpopo company has recorded quarterly maize sales and seasonal ratios from 2015 to 2017 financial year. Table 1 shows quarterly maize production sales with their seasonal ratios (SR). Table 1: Seasonal ratios for maize production sales. Year 2015 2016 Quarter Sales SR Q₁, Q₂, Q3, Q Q₁ ₂ 8, 12, 12, 10 Q₂, Q3, 10, 15, 14, 10 111.63, 87.87 83.33,122.45, 115.42, 84.18 Q4 Use Table 1 to calculate: a) the median seasonal indices (S) and their totals (S). b) the adjusted factor. c) the adjusted seasonal indices (S) and their totals (S.). Q₁ 9 Q₂ 14 2017 " Q3, Q₁ 14, 12 76.60 ,116.67, 113.09, 94.12arrow_forward
- Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningCollege AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningMathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage