I need help on question 1 and 2 only.

The Business of Motion Picture Revenue and DVD Release There has been increasing pressure by mot ture executives to Exercises narrow the gap between theater release of a movie and release In DVD. The executives want to reduce m penses, adapt to 1. A movie executive wants to fit a function to the data. the increasing consumption of on-demand movies, and boost Make a scatterplot of the data points (1. G). then use decreasing DVD sales. Theater owners, on the other hand, want to REGRESSION to fit linear, quadratic, cubic, and expo- protect sales. The owners are fearful that if m cecutives short nential functions to the data, and graph each en the time between theater release and DVD release, the number equation with the scatterplot. Which function fits of ticket buyers will drop, as many people will wait for the DVD best? Why? The table to the right gives the number of days between theater release and DVD release for 10 movies. Note that the 2. Use the exponential function to predict gross rev- average gap in time is about 4 months. enue, G. for weeks 9 through 13. Let's examine the data for Monsters University. The table on the facing page presents the weekly estimates of grass NUMBER OF DAYS revenue, G, for the movie. The total MOVIE RELEASE DATES SEPARATING revenue, R. is approximated by adding RELEASE DATES each week's gross revenue to the Dallas Buyers Club Theater Nov. 1 2013 previous week's total revenue DVD Feb. 4, 2014 12 Years a Slave Theater Oct. 18, 2013 137 DVD Mar. 4, 2014 American Hustle Theater Dec 13 2013 95 DVD: Mar. 18 2014 Lee Daniels' The Butler Theater Aug. 16, 2013 151 DVD Jan. 14, 2014 Captain Phillips Theater Oct 11, 2013 102 DVD Jan. 21, 2014 Rush Theater Sept 20, 2013 130 DVD_ Jan. 28, 2014 Monsters University Theater June 21, 2013 130 DVD Oct. 29, 2013 Man of Steel Theater June 14. 2013 181 DVD: Dec. 12, 2013 Star Trek Into Darkness Theater May 17, 2013 116 DVD Sept. 10, 2013 World War Z Theater: June 21, 2013 DVD: Sept. 17, 2013 Average = 121 days, or about 4 months Source www.imdb com.) 370 Extended Technology Application 371 3. Use your predictions from Exercise 2 to compute Revenue for Monsters University total revenue, R. for weeks 9 through 13. WEEK IN WEEKLY REVENUE G TOTAL REVENUE, # 4. Use REGRESSION to fit a logistic function of the form (current week for cumulative book R(1) = (/(1 + ac ) to the data points (1 R) for office revenue, In 20-26, 2013) millions) weeks 1-8. Based on these results, what seems to be a limiting value for the total revenue from Monsters June 26 $115 33 $115 33 University 2, July 2 $7057 $185.90 3 July 9 $36 09 $221 99 5. Find the rate of change R'(1), and explain what it means Find lim R'(() and explain what it represents. 4. July 16 241 22 5. July 23 59 72 $250.94 6. The DVD release for Monsters University was 6 July 30 53.49 $256.43 October 29, 2013, Based on the given data, do you 7. Aug 6 $2.60 259.09 think this release date was appropriate? What other 8 Aug. 13 51 3 $260.46 factors might influence the release date of a DVD? 9. Aug 20 10. Aug. 27 HI. Sept. 3 12 Sept 10 13 Sept 17 (Source wwwthe-numbers.com Revenue for Dallas Buyers Club WEEK IN WEEKLY REVENUE, TOTAL REVENUE, R RELEASE, tweak G [current week mulative box 1 = November estimates, In office revenue, In 1-7, 2013) millions L Nov 7 $0 35 2 Nov LI 50.9 :1 26 3 Nov. 21 $2 43 $3 69 4. Nov 28 $4.01 7. Now, consider the data for Dallas Buyer's Club 5 Dec. $3.25 $109 shown in the table to the right. This movie was re- 6 Dec 12 $2.18 $1313 leased in selected theaters on November 1, 2013, and 7. Dec. 19 $16 released nationwide (United States and Canada) on H. Dec. 20 $15:45 November 22, 2013. Make a scatterplot of the data 9 Jan 2. 2014 points (f. G) for weeks I through 8, and fit linear, quadratic, cubic, and exponential functions to the 10 Jan 9 data. Which function, if any, best estimates the 1 1. Jan. 16 weekly gross revenue for weeks 9 through 147 12. Jan. 23 13 Jan. 30 8. Make a scatterplot of the data 14. Feb. 6 (week (1. G) for weeks 4 of DVD release)