I just need help on problems 1 and 2.

There has been increasing pressure by motion picture executives to Exercises narrow the gap between theater release of a movie and release to DVD. The executives want to reduce marketing expenses, 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 (t. 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 movie executives 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 gross NUMBER OF DAYS revenue, G, for the movie. The total SEPARATING MOVIE RELEASE DATES RELEASE DATES revenue, R, is approximated by adding 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 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 122 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, R 4. Use REGRESSION to fit a logistic function of the form RELEASE, (current week for cumulative box R(1) = c/(1 + ae ) to the data points (t. R) for (week 1 = June estimates, In office revenue, in 20-26,2013) millions) millions] weeks 1-8. Based on these results, what seems to be a limiting value for the total revenue from Monsters 1 June 26 $115.33 $115 33 University? 2. July 2 $70.57 $185 90 3. Find the rate of change R'(t), and explain what it 3. July 9 $ 36.09 $221.99 $19:23 $241.22 means. Find lim R'(t), and explain what it represents, 4 July 16 5. July 23 59 72 $250.94 6. The DVD release for Monsters University was 6 July 30 $5.49 $256.43 October 29, 2013. Based on the given data, do you 7 Aug. 6 $2.66 $259.09 think this release date was appropriate? What other 8. Aug. 13 $1 37 $260.46 factors might influence the release date of a DVD? 9 Aug 20 10 Aug. 27 11 Sept 3 12 Sept. 10 13. Sept 17 (Source www.the-numbers.com) Revenue for Dallas Buyers Club WEEK IN WEEKLY REVENUE TOTAL REVENUE, R RELEASE, I (week G (current week for cumulative box I'm November estimates, in office revenue, in 1-7, 2013) million) millions I. Nov. 7 $0 35 50 35 2. Nov. 14 $0 91 51 26 3. Nov 21 52 43 53.69 4. Nov. 28 5401 $7.70 7. Now. consider the data for Dallas Buyer's Club, 5. Dec. 5 3:25 $10 95 shown in the table to the right. This movie was re- 6. Dec. 12 $2 18 $13 13 leased in selected theaters on November 1, 2013, and 7. Dec 19 $1.6 $14 77 released nationwide (United States and Canada) on 8. Dec. 26 50:68 $15.45 November 22, 2013. Make a scatterplot of the data points (1, G) for weeks 1 through 8. and fit linear, 9 Jan. 2, 2014 quadratic, cubic, and exponential functions to the 10, Jan. 9 data. Which function, if any, best estimates the 11 Jan. 16 weekly gross revenue for weeks 9 through 14? 12. Jan. 23 13, Jan 30 8. Make a scatterplot of the data 14. Feb. 6 (week of DVD release)