Math assignment
1 Adams, Fall 2020 MAT151 Exam 1 – Chapters 1 & 2 Name: _____________________ INSTRUCTIONS: All responses must be done in complete sentences, include units, and make sense. You can earn partial credit for your work even if the solution is incorrect as long as I can READ your work and it MAKES mathematical sense. EACH QUESTION NOTES TOTAL POINT VALUE AND EACH SECTION NOTES POINT VALUE – 100 POINTS ARE TOTAL FOR EXAM. MAT 151 Exam #1 Academic Honesty and Integrity Besides academic performance, students should exhibit the qualities of honesty and integrity. Every student is expected to produce his/her original, independent work. Any student whose work indicates a violation of the MCCCD Academic Misconduct Policy including cheating, plagiarism, and dishonesty wil l be subject to disciplinary action. Refer to the CGCC Student Handbook (https://www.cgc.edu/sites/default/files/inline/file/3124-2019-2020-catalog.pdf) or website (https://www.cgc.edu/admissions/admissions-records/rights-responsibilities) for information regarding Academic Misconduct and due process procedures. You may use your notes and any other resource that you like while taking this Exam, except for a person. You may not get help from anyone regarding this Exam. Sign below to confirm that you have read the above statements: Print Name Signature Date https://www.cgc.edu/sites/default/files/inline/file/3124-2019-2020-catalog.pdf https://www.cgc.edu/admissions/admissions-records/rights-responsibilities 2 Adams, Fall 2020 1. (10 points) The percent of 16-year-olds with a driver’s license is given below. Year t Percent of 16- Year-Olds with a Driver's Licenses L 1986 46 2003 30.5 2011 27.5 2017 26.0 a. Determine the one-year average rate of change for each consecutive pair of data. (5 Points) b. Write a sentence that interprets one of the average rates of change found in part a in the context of the situation. (5 Points) 2. (20 Points) When eating in a restaurant many people leave a 18% tip. The following function may be used to compute an 18 % tip for a particular restaurant bill: ? = ?(?) = 0.18 ⋅ ? where T is the tip and B is the total restaurant bill. a. Describe what the notation BTf =− )(1 means in this context. b. Solve the equation 15.30 = 0.18? and explain what the result means in the context of the situation. c. The inverse function for this situation is TTf 5)(1 =− . Evaluate ?−1(15.30) and explain the practical meaning of the solution. d. Explain the relationship between the results in b and c. 3 Adams, Fall 2020 3. (15 points) In 2001, North American cruise lines operated 167 ships, and by 2004 the cruise lines increased to 192 cruise ships. Source: Statistical Abstract of the United States, 2007, Table 1245 a. Model the number of cruise ships, C, as a linear function of the year since 2001, t. (5 Points) b. Explain the meaning of the slope using the real-world context of the problem. (5 Points) c. If the number of cruise ships continues to increase linearly, how many will be in operation for 2021? (5 Points) 4. (15 points) According to a height and weight chart a medium- frame adult woman who is 5’4” tall should weigh approximately 130 pounds, and a medium- frame woman who is 5’10” should weigh approximately 150 pounds. Source: http://www.healthchecksystems.com/heightweightchart.htm#frame a. Model the weight of an adult woman, in pounds, as a linear function of height, in inches. b. Explain the meaning of the slope in the context of the problem. c. A medium-frame woman weighs 125 pounds. What will the model estimate her height to be? http://www.healthchecksystems.com/heightweightchart.htm#frame 4 Adams, Fall 2020 5. (20 points) The graph below shows the number of minority students attending ASU between 2006 and 2016. Source: https://uoia.asu.edu/sites/default/files/asu_total_2006-2016_to_post.pdf Years No of Minority Students 2006 14,769 2008 17,334 2010 21,060 2012 23,877 2014 28,292 2016 34,699 a. Using the linear regression, generate a linear model for the graph shown above (align the data so 0t = is 2000). b. Interpret the meaning of the average rate of change and vertical intercept for your model in terms of minority student enrollment. c. Use your model to predict when minority enrollment will reach 36,000 students. What are the limitations of your prediction? https://uoia.asu.edu/sites/default/files/asu_total_2006-2016_to_post.pdf 5 Adams, Fall 2020 6. (20 points) The emphasis on higher education has been increasing over the years, especially among women. a. Write a linear model for the percentage of men, M, as a function of time, t (align the data so 0t = is 1980 and ? = 35 is 2015). b. Write a linear model for the percentage of women, W, as a function of time, t. c. Using both models, in what year will women meet and surpass men in obtaining a bachelor’s degree