4th Order Rurka-Kutta Method This assignment will expand your skills on using Excel to perform some numerical analyses and plot your results. It is a means to familiarize you more with basic features in the spreadsheet. Preliminaries: a. Start a new file called R-K.xlsx (for this exercise, you may use the work you did in class but please be careful not to delete what you already have) b. Plan ahead Exercise 1: Using the 4" Order Ruga-Kutta Method that we recently learned, evaluate the following ordinary differential equation (ODE): dx f(t, x) = = x+t² dt At the initial position, X= 0, the time is = 0.1 minutes. Using a step size of, h = 0.05, what is the time spent to reach a position that is equal to 17 (Hint: use a O and b 1) Exercise 2 Using the 4th Order Ruga-Kutta Method, solve the following problem: The concentration of a certain non-reactive (conservative) chemical is given as a function of time by: de f(t,c) = = 30-3c Where c is the concentration and t is time. At the initial time, to, the concentration in the tank is C. 50 g/L. Using a step size of, h — 0.1875 min, what is the concentration of this chemical after 3 minutes?

Present Example 6.1 in Chapter 6 using the format discussed in Section 4.2. Divide the example problem into Given, Find, and Solution sections.