## Electronic Lab Notebook Week 2

### Purpose

To explore the functions and use of Matlab in creating models and modeling through the execution of two tasks, creating a graph of two vectors and plotting and comparing the growth curves of four various growth rates.

### Methods

• Part I: Create a script that includes the following elements
• Define a vector u containing the elements 1,2,3,4,5,6,7,8,9,10 using the colon operation
• u=1:10
• Define another vector v containing elements that are the square of the vector x
• v=u.^2 Note: include . (dot) when applying arithmetic to a vector
• Plot v versus u using circles on the points that are connected with dashed lines
• figure
• plot(u,v,'--o')
• Save your plot as a TIFF file
• Save your data into an excel spreadsheet using the MATLAB command xlswrite
• filename='name of file.xlsx'
• A=[u;v] Note: need to define A with data set in order to save work to excel sheet
• xlswrite('name of file.xsls',A)
• Part II: Create a script to compare logistic growth curves
• Define a vector t starting at 0, ending at 1, in steps of 0.01.
• t=[0:0.01:1]
• Define K = 10 and x0 = 2 for carrying capacity and initial population size.
• Plot logistic growth curves for growth rates 0.5,1.0,1.5, and 2.0.
• A1=(x0*K)./(K*exp(-0.5*t)-x0*exp(-0.5*t)+x0)
• A2=(x0*K)./(K*exp(-1*t)-x0*exp(-1*t)+x0)
• A3=(x0*K)./(K*exp(-1.5*t)-x0*exp(-1.5*t)+x0)
• A4=(x0*K)./(K*exp(-2*t)-x0*exp(-2*t)+x0)
• Plot these four curves together in one figure, and add appropriate labels, title, and legend.
• figure
• hold on
• plot(t,A1,'color1',t,A2,'color2',t,A3,'color3',t,A4,'color4')
• xlabel('x axis name')
• ylabel('y axis name')
• title('title of graph')
• Note: legend can be created and edited directly on figure
• Save your plot as a TIFF file

### Results

#### Data and Files

##### Graph 1: V vs U
• Figure 1. The figure above displays a plot of vector v versus vector u.
##### Graph 2: Logistic Growth Curves
• Figure 2. The graph above displays the logistic growth curves for four different growth rates with the values r=0.5, 1, 1.5, 2 as color coded and displayed in the legend.

### Conclusion

Through the execution of the two part Matlab exercise, I was able to understand some of the basic functions necessary for creating models on Matlab, thus fulfilling the purpose of the lab. By plotting the two vectors and creating a graphical representation of the four logistic growth curves I was able to engage in the process of modeling by moving observations of a relationship found in the real world, such as the relationship between the number of individuals in a population and the growth rate of that population, into the form of model that acts as a simplified representation of that relationship.

## Acknowledgments

• I worked with my homework partner Margaret J. O'Neil Wednesday night face-to-face in the computer lab to work on parts I and II of the assignment on Matlab.
• In addition, we were joined by Lauren M. Kelly, who worked with us on Part II, creating the graph of the four growth curves.
• Furthermore, Dr. Dahlquist helped me add the BIOL398-05/S17 category to my template and update the links found on my template, which was invoked on this page.
• Methods section is copied and pasted directly from Week 2 Assignment page referenced below.
• Except for what is noted above, this individual journal entry was completed by me and not copied from another source.
• Nika Vafadari 00:04, 26 January 2017 (EST):