(5) It is known from experiment that an initial mass A0 of carbon-14 decays according to the function A(t) = A0e kt with k = 0000120. This constant k is the particular value associated with carbon-14. (a) Show using a derivative that the rate of decay of carbon-14 is always directly propor tional to the amount present. (This means the rate of decay should be equal to some constant times the amount present at time t.) (b) Suppose a famous painting was carefully analyzed and found to have 94.0% to 94.5% of its original carbon-14 remaining from the time it was painted. Estimate an age range for this painting