Problem 4 (20%): A common function to explain the ion channel dynamics in cell membranes is r(v) = ln(3+4v) where v is the membrane potential and r(v) describes the response of the channel to a given voltage. To visualize different approximations of the channel response, approximate it with 1, 2, 3, 4, and 5-term (n = 0,1,2,3,4) Taylor series expansion about a membrane potential of zero; Then plot each expansion and the exact value of (v) on a single axes around the typical range of membrane potentials, v= -1 to v = 1. Label your axes and indicate what each curve represents (consider the "legend" command). Problem 5 (15%): The following is a 64 bit double precision floating- point number: 11000000010110101100000000000000000000000000 00000000000000000000 a) Calculate the exponent component, e b) Calculate the mantissa c) Calculate floating-point number, in decimal