Please use MATLAB to solve the questions.

The related content is also provided in the .zip file.

 

Extra Credit for Midterm (10pt) A very powerful approxima:on for π was developed the following series: 1.  Write a func:on of above series and name “fn_PIseries.m” 2.  Write a script which input N and display the result for fn_PIseries.m. The script should also compare the difference between the actual pi and display the result. Output for N=30 and 100. Script name should be “PI_series.m” Extra Credit 1 (5pt) •  To analyze electric circuits, it is oUen necessary to solve simultaneous equa:ons. To find the voltages Va, Vb, and Vc at nodes a, b, and c, the equa:ons are: –  2(Va-Vb) + 5(Va-Vc) – e-t = 0 –  2(Vb – Va) + 2Vb + 3(Vb – Vc) = 0 –  Vc = 2 sin(t) •  Find out how to use the solve func:on to solve for Va, Vb, and Vc so that the solu:on will be returned in terms of t. Submit your work in diary (or doc) file. Extra Credit 2 (5pt) The reproduc:on of cells in a bacterial colony is important for many environmental engineering applica:ons such as wastewater treatments. The formula log(N) = log(N0) + t/T log(2) can be used to simulate this, where N0 is the original popula:on, N is the popula:on at :me t, and T is the :me it takes for the popula:on to double. Use the solve func:on to determine the following: if N0 = 102, N = 108, and t = 8 hours, what will be the doubling :me T? Use double to get your result in hours. Submit your work in diary (or doc) file.