2. The half-life of radioactive isotope Rhodium-101 is 3.3 years. This means that after 3.3 years, there will be half of the original atoms present. The number of Rhodium atoms present at any time can be modelled using the function R(t) = Roe-kt , where Ro is the number of original atoms present (Ro = R(0)), k is a decay constant and t is the number of years after the measurements began. (i) Determine the decay constant k. (ii) How many atoms remain after 13.2 years? (iii) At what time has 90% of the Rhodium-101 atoms decayed? (iv) Sketch a graph of the atoms present against time. 3. A harmful algal bloom was discovered in an inland lake recently. The area, A(t), of the bloom t hours after it was first discovered can be modelled by A(t) = M + N In(t2 + 1). When first discovered the algal bloom had an area of 96 m. Three hours later the area of the bloom was 144 m. (i) Determine the values of the constants M and N. (ii) What is the area of the algal bloom 7 hours after discovery? (iii) When did the bloom have an area of 170 m? (iv) Sketch A(t) over the domain 0