Math 115 Practice for Exam 1 Generated September 7, 2017 Name: Instructor: Section Number: 1. This exam has 4 questions. Note that the problems are not of equal difficulty, so you may want to skip over and return to a problem on which you are stuck. 2. Do not separate the pages of the exam. If any pages do become separated, write your name on them and point them out to your instructor when you hand in the exam. 3. Please read the instructions for each individual exercise carefully. One of the skills being tested on this exam is your ability to interpret questions, so instructors will not answer questions about exam problems during the exam. 4. Show an appropriate amount of work (including appropriate explanation) for each exercise so that the graders can see not only the answer but also how you obtained it. Include units in your answers where appropriate. 5. You may use any calculator except a TI-92 (or other calculator with a full alphanumeric keypad). However, you must show work for any calculation which we have learned how to do in this course. You are also allowed two sides of a 3 5 note card. 6. If you use graphs or tables to obtain an answer, be certain to include an explanation and sketch of the graph, and to write out the entries of the table that you use. 7. You must use the methods learned in this course to solve all problems. Semester Exam Problem Name Points Score Winter 2015 1 8 squirrel chase 2 10 Winter 2006 1 6 fresco 11 Fall 2015 1 7 chocolate 12 Fall 2013 1 1 foot size 14 Total 47 Recommended time (based on points): 42 minutes
Math 115 / Exam 1 (February 10, 2015) page 8 8. [10 points] Throughout this page, give all answers in exact form. Do not use decimal approximations. For example, x = 1 3 is an exact solution to 3x = 1, but x = 0.3333333333 is not. Sebastian has rented a helicopter to catch up to his friend Erin who is currently chasing a suspected criminal named Elphaba. When Sebastian first sees the pair they are 180 meters apart. After 3 minutes, Erin has moved 60 meters closer to Elphaba. (In other words, the distance between them has decreased by 60 meters.) Let D(t) be the distance between Elphaba and Erin, in meters, t minutes after Sebastian begins watching them. a. [2 points] Sebastian initially assumes that D(t) is a linear function. Find a formula for D(t) under this assumption, valid for as long as it takes for Erin to catch Elphaba. Answer: D(t) = b. [1 point] After Sebastian has been watching for 6 minutes, the distance between Erin and Elphaba is 80 meters. Briefly explain why this contradicts Sebastian s initial assumption. c. [4 points] Sebastian then determines that D(t) must in fact be an exponential function. Write a new formula for D(t) given this new information (including the data from part (b)). Remember to show your work carefully and use exact form. Answer: D(t) = d. [3 points] Erin can catch Elphaba when she is within one meter of her (since Erin can jump and tackle Elphaba at this distance). Use algebra and your formula from part (c) to find how long it takes for the distance between Erin and Elphaba to decrease to 1 meter. Answer: Winter, 2015 Math 115 Exam 1 Problem 8 (squirrel chase 2)
6 6. (11 points) A fresco supposedly painted by the Italian Renaissance artist Alessandro Botticelli (1445-1510) currently contains 92% of its carbon-14 (half-life 5730 years.) From this information, decide whether Botticelli could have painted the fresco. Show step-by-step calculations, and briefly explain your conclusion. Winter, 2006 Math 115 Exam 1 Problem 6 (fresco)
Math 115 / Exam 1 (October 13, 2015) page 7 7. [12 points] Phillip Asafy and Genevieve Omicks both enjoy hot chocolate when it s cool outside. They made a few measurements, and these appear in the table below. P (respectively G) is Phil s (respectively Gen s) consumption of hot chocolate (in quarts, measured to the nearest tenth of a quart) in a month when the average daily high temperature is H (in degrees Celsius, measured to the nearest degree). H( C) P (quarts) G (quarts) 3 16.1 13.3 7 12.8 11.6 15 8.0 6.5 a. [8 points] Based on this data, could either student s monthly hot chocolate consumption be reasonably modeled as a linear function of average daily high temperature? An exponential function? Neither? Carefully justify your answer in the space below. (Hint: At least one of these can be modeled by a linear or an exponential function!) Answers: Circle one choice for each student. Phil s consumption P: linear exponential neither linear nor exponential Gen s consumption G: linear exponential neither linear nor exponential b. [4 points] For this investigation, their friend Maddy measures temperature in degrees Fahrenheit, and she measures her hot chocolate consumption in cups. She finds a function M(f) which is the number of cups of hot chocolate she consumes in a month when the average daily high temperature is f degrees Fahrenheit. If Q(H) is the number of quarts of hot chocolate Maddy consumes when the average monthly temperature is H degrees Celsius, write a formula for Q(H) in terms of M and H. Recall that there are 4 cups in a quart and that the conversion from Fahrenheit to Celsius is given by y = 5 9 (x 32) (where y C and x F describe the same temperature). Answer: Q(H) = Fall, 2015 Math 115 Exam 1 Problem 7 (chocolate)
Math 115 / Exam 1 (October 8, 2013) page 2 1. [14 points] Carla is trying to model the growth of the feet of her son, Taser, to predict what size boots she needs to buy him to last him through the winter. She has measured Taser s feet three times, once exactly nine months ago, once exactly three months ago, and once just today. Carla decides to measure t in months since she took her first measurement. Below is a table containing her measurements. Carla lost the record of her first measurement so the corresponding entry in the table is blank. t (months) 0 6 9 foot length (inches) 6.4 7.2 a. [3 points] Write a linear function L(t) modeling the length of Taser s feet t months after she took her first measurement. b. [5 points] Write a exponential function E(t) modeling the length of Taser s feet t months after she took her first measurement. c. [2 points] According to the exponential model you found in (b), what is the missing value in the table above? d. [4 points] Bob, the salesman at the shoe store, has a different model for foot growth. He gives Carla the formula 50 B(t) = 5+6e t/8 for the length of Taser s feet t months since Carla took her first measurement. According to Bob s model, when will Taser s feet be 8 inches long? Give your answer in exact form with no decimals. Fall, 2013 Math 115 Exam 1 Problem 1 (foot size)