Background: The amount of two unknown substances s; and 2 over time t is described by Si = 5e-0.5t S2 = 1 + 2 sin(0.17tt) As a check 51 -1.8394 and 52 = 2.1756 when t = 2. 1 3 of 45 : (a) Use the false-position method to determine the time when s1 = 1. Use initial guesses of t = O and ty = 20 seconds and a precision of 0.001. Also, provide the number of iterations taken Provide your answers to 4 decimal places as printed by MATLAB The time required for sy=1 [4dp] = [2 marks] . Number of iterations = [2 marks] 1 : Notes + 1 Unsure 1 Marks (b) Use fzero() to determine the times for when s2 = 2. There should be two solutions over the range of Osts 20. Provide your answers to 4 decimal places as printed by MATLAB Mark (b) Use trero () to determine the times for when 52 = 2. There should be two solutions over the range of Osts 20. Provide your answers to 4 decimal places as printed by MATLAB + Lower time value for when sz=2 [4dp= [2 marks] Higher time value for when sz=2 (4dp] = [2 marks] Notes Mark (c) Consider the following initial guesses of tand tu. L 10, 10, 15, 30, 35, 50, 551 tu - 15. 15, 20, 35, 40, 55, 603 Write a MATLAB code to determine the intersection points between the sand s2 equations using the above guesses and the following conditions: 1. A for loop must be used 2 Bisection method must be used with a precision of 0.01 3. Use vectors to store the root and iteration values determined for each bracket pair. 4 Determine the t_ that requires the least number of iterations to converge within the precision of the solution. Provide the number of iterations. Also determine the corresponding root (time) value Provide your answers to 4 decimal places as printed by MATLAB 45 1 [2 marks] The te value that requires the least number of iterations = [2 marks] Number of iterations for the above t value = 12 marks] Number of iterations for the above t value = [2 marks] Corresponding root (time) value (40p) = [2 marks] Copy and paste your MATLAB code into the textbox of the next question. Copy and paste your MATLAB code for part (c) in the previous question in the plain text box below. You can also upload your m-file below (optional). [6 marks] c B 1 X2 x !!! III . DF Maximum size for new files: 268, maximum attach Background: The amount of two unknown substances s; and 2 over time t is described by Si = 5e-0.5t S2 = 1 + 2 sin(0.17tt) As a check 51 -1.8394 and 52 = 2.1756 when t = 2. 1 3 of 45 : (a) Use the false-position method to determine the time when s1 = 1. Use initial guesses of t = O and ty = 20 seconds and a precision of 0.001. Also, provide the number of iterations taken Provide your answers to 4 decimal places as printed by MATLAB The time required for sy=1 [4dp] = [2 marks] . Number of iterations = [2 marks] 1 : Notes + 1 Unsure 1 Marks (b) Use fzero() to determine the times for when s2 = 2. There should be two solutions over the range of Osts 20. Provide your answers to 4 decimal places as printed by MATLAB Mark (b) Use trero () to determine the times for when 52 = 2. There should be two solutions over the range of Osts 20. Provide your answers to 4 decimal places as printed by MATLAB + Lower time value for when sz=2 [4dp= [2 marks] Higher time value for when sz=2 (4dp] = [2 marks] Notes Mark (c) Consider the following initial guesses of tand tu. L 10, 10, 15, 30, 35, 50, 551 tu - 15. 15, 20, 35, 40, 55, 603 Write a MATLAB code to determine the intersection points between the sand s2 equations using the above guesses and the following conditions: 1. A for loop must be used 2 Bisection method must be used with a precision of 0.01 3. Use vectors to store the root and iteration values determined for each bracket pair. 4 Determine the t_ that requires the least number of iterations to converge within the precision of the solution. Provide the number of iterations. Also determine the corresponding root (time) value Provide your answers to 4 decimal places as printed by MATLAB 45 1 [2 marks] The te value that requires the least number of iterations = [2 marks] Number of iterations for the above t value = 12 marks] Number of iterations for the above t value = [2 marks] Corresponding root (time) value (40p) = [2 marks] Copy and paste your MATLAB code into the textbox of the next question. Copy and paste your MATLAB code for part (c) in the previous question in the plain text box below. You can also upload your m-file below (optional). [6 marks] c B 1 X2 x !!! III . DF Maximum size for new files: 268, maximum attach
