Let y(t) be the percentage of the population that supports a particular government policy. The rate of change of the level of support for the policy is proportional to both the percentage of the population that agrees with the policy and the percentage that disagrees with the policy. Let the constant of proportionality for this relationship be written as k. (a) Enter the differential equation that is satisfied by y. (Your answer should be given in terms of y. Even though y is a function of time, enter y, rather than y(t).) dy dt = (b) Suppose that k is positive. Sketch a number of solutions of the differential equation, starting from a range of initial levels of support for the policy. (This will not be graded.) (c) Suppose that k is negative. What do solutions of the differential equation now look like? What happens to the level of support for the policy? (This will not be graded.) (d) Now, suppose that, in addition to people changing their support as described above, people also change from agreeing to disagreeing because they have second thoughts about the policy. Suppose that this rate is proportional to the percentage of people that agree with the policy, with constant of proportionality equal to c. Enter the new differential equation that is satisfied by y. dy = dt