The answer is shown below; please explain the intuition/process/formula used to derive these functions. Thank you.

2. (5 points) A Risky Investment: Suppose that you have the opportunity to invest r dollars in a risky asset. In the good state of the world, the asset pays a return of 30% and in the bad state of the world the asset pays a return of -20%. Suppose that there is a 50% chance that we will be in the good state of the world and the utility function is u(w) = who W , where o = 2. Additionally, the consumer's wealth is w = $100. (a) Find the consumer's wealth in the good and bad state of the world as a function of the amount invested in the asset. W. = (100 - x) + x(1+.3) = 100 + 0.3x Wb = (100 - x) + x(1 -0.2) = 100 - 0.2x (12)