PartA You have been given a set of data that can be found at h_ttpswfwwwdesmoscomfcalcu latorfdwucmx M and it is yourjob to come up with an accurate mathematical model for the entire equation. The data is listed in a Table that you should not edit it in any way. If you do edit it, you will have to reopen the link, and start over again. You will be creating a piecewise function that is made up of some of the functionswe have studied in this course. which functions you use, and where you use them is completely upto you, the end goal is to create a model that could be used to accurately describe the data. The functions we have studied {and their general form} that you are free to use are: 0 Polynomials: I] I] D D D Etc. 0 Rational Functions I] where and are both polynomial functions 0 Radical Functions I] o Exponential Functions I] o Logarithmic Functions D In each of the general forms the letters a. b, c, d, e, simply represent the constants that will dene the shape of the function. STEP 1: Analyze the graph. and nd a portion of it that looks like it could be dened by a single function. STEP 2: Input the general form of that function as a new expression in DESMOS, and add a slider for each of the constants. STEP 3'. Adjust the sliders until you have matched the graph as best you can to that section of the data. STEP 4: Restrict the domain of your function on DESMOS so that the function only appears over the appropriate section of the data. STEP 5: Record all of your findings in the chart on the following page. STEP 6: Find another portion of the graph that could be defined by a single function and repeat steps 2 through 6, until you have a function for each portion of the graph. I have assumed that you have used no more than four single functions to define the entire set of data. However, it is possible to use fewer than four functions. As a result you may have some rows in this chart blank. *Be sure that your domains DO NOT overlap unless the two individual functions meet at the same point. [16] The general form of the function The values of the constants The domain for this function A picture of this area of the graph Example six ) = ax+ b -2 Your Solution Click or tap here to enter text. | Click or tap here to enter text.Click or tap here to enter text. | Click or tap here to enter text. Click or tap here to enter text. | Click or tap here to enter text.Click or tap here to enter text. | Click or tap here to enter text. Now piece it all together to give a functions that models all the data! [4] Function Graph Example20 * + 3.8 , - 54 x 6 1 -10 21 7 ( x - 4 - 2) - 4.9 16 * 6 7 0 -10 Your Solution Part B Consider the data found at https://www.desmos.com/calculator/kufbiixOfyUsing the same methods as Part A, you will create two models for the data. The first model will use a single rational function. The second model will use two exponential functions. Follow the steps below as a guide: STEP 1: Create a rational function in DESMOS of the form and add sliders for all letters STEP 2: By experimenting with values for , , and , find a function that accurately models the data STEP 3: Record your findings in the chart that follows STEP 4: Remove the rational function, and all associated sliders STEP 5: Create two exponential functions in DESMOS of the form and and add sliders for all letters STEP 6: By experimenting with the values for , . . . . , , , and , find the two functions that accurately model the data STEP 7: Record your findings in the chart below STEP 8: Answer the follow-up question [6] Rational Function Exponential Functions Function type &Model (i.e. the function/functions with specific values Graph If done correctly, you should have been able to make both models fit the data fairly closely. [4] Hopefully this made you realise that a rational function of this form, and a piecewise function made of two exponential functions are very similar to one another; same curvature, same areas of increase/decrease. There is however one major difference between the two options for the model; the rational function has one property that the exponential ones do not.a) Discuss this difference between these two models and the effect it would have for a person trying to decide which model to use (HINT: consider reviewing the definition of a function). Click or tap here to enter text. b) Create a piecewise function for the model that is made of the two exponential functions. Be sure to limit the domain of the pieces so that it this functions domain matches the domain of the model produced by the rational function.MATH 1319 Click/tap here and enter your first and last name. Functions Modelling Project Click/tap here and enter your first and last name. The goal of this project is to introduce you to mathematical modelling in its most primitive sense. Throughout the project you will spend time trying to fit functions to a data set. In reality, there are sophisticated algorithms that can be used to find the best model for a data set, but we explore those in this course (just know they are there). Your main tool for creating your models will be a free online graphing software called DESMOS. Whether you are unfamiliar with DESMOS, or a seasoned pro, please watch the intro video I have created and posted on DC Connect. The video can be found in the Assignment Folder for this project. This video provides an overview of how to complete the tasks you will be asked to do in this project. I suggest creating a profile on DESMOS. It is free, only requires an email, and allows you to save your graphs as you work on them. Without the ability to save your graphs, you run the risk of losing your work if your browser is ever closed ** *All of your work will be done either on DESMONS or written on paper by hand, but your final submission will only be this document. You will take screenshots of the graphs you create in DESMOS and insert them to the appropriate parts of this document. Likewise, you will take clear pictures of the work you do by hand and insert them into the appropriate parts of this document. Part A: Part B: 20 10 Total: 30