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1. You invest an initial capital of 10,000 euros at the beginning of 2020 and an additional 1,000 euros at the beginning of the following years. You also get an annual return of 5.1 percent on your investment, which is rounded to the nearest centimeter. Table the value of your investment at the beginning of each year until 2070, starting from 2020. Save the table in the variable ''arvo''. 2.Compute an estimate for exp(2) using MacLaurin's series (Eq 1) the first five terms. Store the result in the variable result. Also calculate the error of this estimate compared to the exact value you get using the exp function of the math module. Store the error in the variable error. The factor is available from the math module as math.factorial(). 3.The noise in the data in the previous task is just small enough that the trivial trigger works. Now let's look at the data file filtteri.txt. Now there is so much noise in the signal that a simple frequency determination is understandably not possible. Perform low-pass filtering on the signal to reduce noise. The low-pass filtered signal is obtained from Eq (Eq 2) where x is the original signal and the coefficient (Eq3) Here, ?T is the sampling period, i.e. the time between samples. Now this time is constant, so you can calculate it as the difference between the times of the first two samples ?T=t_1 - t_0 . Time constant (Eq4) depends on the cutoff frequency f(c) of the filter. Set the cutoff frequency to 10 kHz. Graphically represent the original signal and the filtered signal in the same image. Note that due to the recursion in the calculation of the signal y, the above formula cannot be used to calculate the value of y(0). You can assume that y(0)=0. The reading of the file has already been completed. Your task remains to change the for loop so that the signal y can be calculated as shown.