1015SCG_MathAssignment_T32023

1015SCG Quantitative Reasoning Maths and inference assignment Maths and Inference Assignment 1015SCG Quantitative Reasoning Trimester 3 2023 Weight: 30% Due date: By Friday 22 nd December 2023 (End of week 7) Name: Student number: Third-to-last digit of student number: Use this to determine which data set to use for Question 1. eg digit is 3, use bac3.csv; digit is 0, use bac0.csv. Write this at the top of your answer to Question 1. Second-to-last digit of student number: Use this to determine which data set to use for Question 2. eg digit is 5, use life5.csv, digit is 0, use life0.csv Write this at the top of your answer to Question 2. Last digit of student number: Use this to determine which data set to use for Question 3. eg digit is 7, use workshop7.csv, digit is 0, use workshop0.csv Write this at the top of your answer to Question 3. Instructions:  Please fill out the above information and enter your answers in this Word document .  If your submission is not in the format provided in this Word document, it will not be graded.  Please upload your final assignment as PDF to the submission point on the course site.  Use the correct csv file, if you use a different file, there will be mark penalty.  For each of the questions show your working – explain how the calculations are done, what software and functions are used, show appropriate screenshots from the software.  Make sure all the plots have titles or captions, axes labels with units and a legend if applicable. The scatter plots should be used for discrete data, lines should be used for fits.  Pay attention to significant figures, especially when quoting the values with errors.  The assignment is out of 100 marks. Marks for each question are given with the question in square braces [ ] .  If you have any questions, please ask your demonstrators during the workshops or post your questions (but not answers or solutions) in the course Teams channel. Page 1 of 8 Your name here sxxxxxxx X X X

1015SCG Quantitative Reasoning Maths and inference assignment Question 1 [40 marks] A lab has 10 different bacterial samples, but they all got mislabelled. The growth of the bacteria in specific conditions is given by an exponential function N ( t ) = N 0 e kt , where N 0 is the initial number of bacteria (for the time t = 0 ¿ , N ( t ) is the number of bacteria after time t (measured in days), and k is the growth constant. Values of the growth factor k are different for each type of bacteria and are given in the table. Bacteria type Growth factor k (1/days) Dangerous level C (number of bacteria/cm 3 ) A 0.11 200 B 0.12 310 C 0.13 500 D 0.14 720 E 0.15 550 F 0.16 1020 G 0.17 1300 H 0.18 1560 I 0.19 2000 J 0.20 2500 You are given a random sample in the Petri dish with initially 100 organisms living in a jelly, and you are asked to determine which type of the bacteria it is. You decide to grow the sample, measuring the number of bacteria in your sample every day. Use the file bacx.csv, where x is third-to-last digit of your student number. a) Plot the number of bacteria as a function of time. [5 marks] b) We want to use regression on this data to find the values characterising the sample growth, but to do it we need linear data. What can you plot on the y axis instead the number of the organisms, so the plot becomes linear? Explain and show appropriate equations. [5 marks] Page 2 of 8 Enter your answer here, expand the text box as needed. Enter your answer here, expand the text box as needed.xx