Ryan Ward

a) dr(t)/dt = -λr(t) =>∫[ dr(t)/r(t) ] = ∫[ -λt ] => ln |r| = -λt + C => r(t) = e^(-λt + C) = e ^ (C - λt) => r(t) = e^C * e ^ (-λt) let C = e^C => r(t) = Ce^(-λt) b) r(0) = r_0 =>r(0) = r_0 = Ce^(-λ(0)) =>r_0 = C =>r(t) = r_0 * e^(-λt)