Following question requires to use Euler's method of approximation and compare to the solution already provided:

The temperature T of a cooling object drops at a rate that is proportional to the difference T C, where C is the surrounding constant temperature. dT dt _ k(T C) We will solve this differential equation to find T(t), but the only function that satisfies this is A cup of coffee at 190 F is left in a room of 70 F. At time t = 0, the coffee is cooling at 15 F per minute. a) Find the function that models the cooling of the coffee. b) How long will it take for the temperature to reach 143 F?\fb) How long will it take for the temperature to reach 143F? TH) = la 645.09}... 70 6. Analyze the problem as in the video, but using your Euler's Method Solution instead of the solution obtained in the video. How does your Euler's Method Solution compare to the actual solution? Your language should include an interpretation of the variables used in the problem. How you compare the solutions is up to you. You could plot the actual solution on your direction field for comparison, or compare output yvalues, but your discussion should refer back to what the variables in the problem mean with respect to the considered application. 3. Choose a step size h different from anyone else's for your chosen problem, and small enough to yield useful results. Use Euler's method with your chosen step size to find an approximate solution to the initial value problem, and make sure you take enough steps to include the t and y values requested in the problem. Use this Euler's Method Spreadsheet for differential equations of the form y' = f(t, y), changing the fields as appropriate to accommodate your function to perform Euler's method. Include a screenshot of your Euler's Method spreadsheet showing your results. 4. Graph 3 direction field for this problem that accommodates the initial value and any final values present in the problem. For example, if the problem has initial condition y(0) = 5, and you are looking for y(10), you will need to include tvalues from at least 0 to 10, and yvalues to accommodate the solution curve between [=0 and t=10. Space your direction field out so that you have at least 100 slopes showing on it. Use this free Desmos program. 5. Plot your Euler's method solution on the same direction field: In Desmos, here are instructions on how to add line segments. To add your table, you can copy the table data from your spreadsheet directly into the next available Desmos field