Radioactive decay occurs when a radioactive isotope ("parent" isotope) gradually transforms into a radiogenic isotope ("daughter" isotope) over time. This process is modeled by the following function: where r is the ratio of parent to daughter atoms, t is time and τΗ is called the halflife. The following table shows several parent-daughter pairs along with their half-lives. Daughter N14 Srs7 Ar4o Pb206 Pb207 Half-Life (years) 5730 48.8 x 109 1.3 x 109 4.6 x 109 0.7 x 10 arent Rbs7 U238 Uz3s Part 1: Creating a UDF (10 points) Open a new script file and save it as L07.m (2 pts) Load the data from the ASCII file C14.dat. The first column of the dataset is a set of times in years. The second column of the dataset are measurements of C14/N14 ratio. (8 pts) At the bottom of your script, create a User-Defined-Function PDratio.m to compute Equation (1). The function must have the following input/output arguments: INPUT 1. 2. 3. the time as an array tau the half-life OUTPUT ran array of the parent-daughter ratios for the times array t, according to Equation (1). Use elementwise operation. . Part 2: Plotting Theory vs. Data (13 points) (11 pts) On a single figure window with the same axes, do the following: (3 pts) Plot the data from the ASCII file (ratio vs time) for the experimental measurements. No line, black diamond markers, marker size 8 a. b. (3 pts) Create a vector t th from 0 to 20000 with 1000 elements and use your function PDratio.m in order to determine the ratio r for C14/Nia and assign it to a variable r_th. Use the half-life data required for the function from the table. Plotr th vs t th on the same figure using - Black solid line, line width 2, no marker (2 pts) Label the x-axis and y-axis with "Time (years)" and "Parent-Daughter Ratio" respectively. (1 pt) Title the figure as "Carbon-14 Radioactive Decay" (2 pts) Add legend with the labels "Experimental data" and "Theoretical data" c. d. e. (2 pt) Use PDratio.m to create arrays for the other 4 parent-daughter pairs. Create a new time vector (t2) from t 0 to t 15x109 years with 100 points and use vour function 4 times with different half-life from the table to determine the corresponding ratio arrays. Create a second figure with a single axis and do the following 1. 2. (1 pt) Plot a dotted, black curve, with no marker and a line width of 1 showing the parent-daughter ratio of Rbs7 to Srs7 (1 pt) Plot a dash-dotted, black curve, with no marker showing the parent daughter ratio of U23s to Pb206 (1 pt) Plot a dashed, black curve, with no marker showing the parent daughter ratio of Kso to Arso (1 pt) Plot a solid, black curve, with no marker showing the parent-daughter ratio of Uz3s to Pb207 (2 pts) Label thex- and y-axes with "Time (Ga)" and "Parent-Daughter Ratio" respectively (1 pt) Title the figure as "Long-Lived Radioactive Isotopes" (2 pts) Add a legend at the upper-right, outside the axis, and label the graphs as follows: "Rubidium-Strontium", "Uranium-Lead (238-206)", "Potassium Argon" and "Uranium-Lead (235-207)" a. b. c. d. e. f. g. Radioactive decay occurs when a radioactive isotope ("parent" isotope) gradually transforms into a radiogenic isotope ("daughter" isotope) over time. This process is modeled by the following function: where r is the ratio of parent to daughter atoms, t is time and τΗ is called the halflife. The following table shows several parent-daughter pairs along with their half-lives. Daughter N14 Srs7 Ar4o Pb206 Pb207 Half-Life (years) 5730 48.8 x 109 1.3 x 109 4.6 x 109 0.7 x 10 arent Rbs7 U238 Uz3s Part 1: Creating a UDF (10 points) Open a new script file and save it as L07.m (2 pts) Load the data from the ASCII file C14.dat. The first column of the dataset is a set of times in years. The second column of the dataset are measurements of C14/N14 ratio. (8 pts) At the bottom of your script, create a User-Defined-Function PDratio.m to compute Equation (1). The function must have the following input/output arguments: INPUT 1. 2. 3. the time as an array tau the half-life OUTPUT ran array of the parent-daughter ratios for the times array t, according to Equation (1). Use elementwise operation. . Part 2: Plotting Theory vs. Data (13 points) (11 pts) On a single figure window with the same axes, do the following: (3 pts) Plot the data from the ASCII file (ratio vs time) for the experimental measurements. No line, black diamond markers, marker size 8 a. b. (3 pts) Create a vector t th from 0 to 20000 with 1000 elements and use your function PDratio.m in order to determine the ratio r for C14/Nia and assign it to a variable r_th. Use the half-life data required for the function from the table. Plotr th vs t th on the same figure using - Black solid line, line width 2, no marker (2 pts) Label the x-axis and y-axis with "Time (years)" and "Parent-Daughter Ratio" respectively. (1 pt) Title the figure as "Carbon-14 Radioactive Decay" (2 pts) Add legend with the labels "Experimental data" and "Theoretical data" c. d. e. (2 pt) Use PDratio.m to create arrays for the other 4 parent-daughter pairs. Create a new time vector (t2) from t 0 to t 15x109 years with 100 points and use vour function 4 times with different half-life from the table to determine the corresponding ratio arrays. Create a second figure with a single axis and do the following 1. 2. (1 pt) Plot a dotted, black curve, with no marker and a line width of 1 showing the parent-daughter ratio of Rbs7 to Srs7 (1 pt) Plot a dash-dotted, black curve, with no marker showing the parent daughter ratio of U23s to Pb206 (1 pt) Plot a dashed, black curve, with no marker showing the parent daughter ratio of Kso to Arso (1 pt) Plot a solid, black curve, with no marker showing the parent-daughter ratio of Uz3s to Pb207 (2 pts) Label thex- and y-axes with "Time (Ga)" and "Parent-Daughter Ratio" respectively (1 pt) Title the figure as "Long-Lived Radioactive Isotopes" (2 pts) Add a legend at the upper-right, outside the axis, and label the graphs as follows: "Rubidium-Strontium", "Uranium-Lead (238-206)", "Potassium Argon" and "Uranium-Lead (235-207)" a. b. c. d. e. f. g.