dP / dt = P / 10 We apply separable variables: dP / P = dt / 10 We integrate both sides: Ln (P) = t / 10 + C We rewrite the equation: Exp (Ln (P)) = Exp (t / 10 + C) P = Exp (C) * Exp (t / 10) P = C * Exp (t / 10) We look for the constant using: P (0) = 300 300 = C * Exp (0/10) 300 = C * 1 C = 300 We rewrite the equation: P = 300 * Exp (t / 10) After 40 hours we have: P = 300 * Exp (40/10) P = 16379.44501 Answer: the population size after 40 hours is: P = 16379
