Question 5: 28 Marks (5.1) Assume that a radioactive substance decays with a constant of decay k = 0.001 when time ismeasured in years. (5.1.1) How long does it take for the substance to decay from 30 grams to 3 grams? (5.1.2) What is the half-life of the substance? (5.1.3) If 20% of an original quantity No is present today, when was No formed initially? (5.1.4) Explain why in (5.1.3) above, we do not need to know the exact value of No. (5.2) Assume that P (t) follows logistic growth, with initial value Po = 200, a = 0.2 and b = 0.085. (5.2.1) Determine P (1) and P (5). (5.2.2) Determine the rate of change of P at the times t = 0, t = 1 and t = 5. (Remember that therate of change is the value of dp/dt). (5.2.3) Draw the phase line of this population model.