blem 4: Cesium-137 is an isotope of cesium that is a common product of fission in a nuclear reactor. The rate of change in the amount of any radioactive substance is proportional to the amount present. Let C denote the amount of cesium-137 remaining in spent nuclear fuel rods after t years. a. Using r for the proportionality constant, write an equation of change for C. b. Solve the equation from part (a). Use Co for the initial value. c. The half-life of cesium-137 is 30.14 years. Use this information to find the value of the proportion- ality constant r from parts (a) and (b). Give the exact value, and then round it to three decimal places. d. How long does it take for the amount of cesium-137 to decay to one-tenth of the initial amount? Round your answer to the nearest year.