In this lab you will again work as individuals, but discussions are OK. The assignment is due at the beginning of lecture on Monday, 30 Mar. In this lab you'll explore the properties of curve-fitting algorithms. You'll need to submit your codes, plots and answers to the questions, below.

1. For this problem, you'll need the data set lab6_1.mat. These represent velocity (m/s) data from an acoustic ranging device as a function of time (s). Use the normal equations method to determine the best fit line for the model equation v = v_o + at.
   • Plot the raw data and a best-fit line on the same axes.
   • State the values determined for v_o and a.
   • Determine the uncertainties in those parameters.
   • Describe a physical experiment that might produce these data.
2. For this problem, you'll need the data set lab6_2.mat. These data represent the signal voltage (V) across a circuit element as a function of time (s). Use the normal equations method to determine the best fit curve for the model equation s = Asin(t) + Bsin(2t) + Csin(3t).
   • Plot the raw data and a best-fit curve on the same axes.
   • State the values determined for A, B and C.
   • Determine the uncertainties in those parameters.
   • Look at your result for B. What change could you make to your model equation based on this result.
3. For this problem, you'll need the data set lab6_3.mat and my code expFit.m. In a lab you have a sample of ¹¹⁶Xe gas. You have a device to determine the amount of that particular isotope present and let it run for a few seconds prior to t = 0 (all t data are in s; N are in # of ¹¹⁶Xe atoms). ¹¹⁶Xe gas naturally decays and you're trying to determine the half-life.
   • What is the half-life of ¹¹⁶Xe according to your data?
   • Did your lab technician properly set up your equipment? Use your fitted parameters to justify your answer.