A is being converted into a compound B over time. The rate of the reaction, in moles per liter per second, is given by the equation: r(t) = (k + e^(-kt)) / (1 + e^(-kt)) where t is the time in seconds, k is a positive constant, and e is the base of the natural logarithm. a) Determine the limit of the rate of reaction as t approaches infinity, i.e., find the value of Lim(t->) r(t). Express your answer in terms of k. b) Find the value of k that maximizes the initial rate of reaction, r(0). c) Given that the concentration of compound A at t = 0 is 1 mole per liter, calculate the time it takes for the concentration of compound A to decrease