Question: 2. Suppose a grows at a constant rate gr = 5 percent per year. Similarly, y grows at a constant rate gy = 1 percent

2. Suppose a grows at a constant rate gr = 5 percent per year. Similarly, y grows at a constant rate gy = 1 percent per year. Suppose the value for at at time t = 0 is equal to 3 (that is, ro = 3), and that the value for ye at time t = 0 is equal to 2 (that is, yo = 2). Finally, suppose z, = 20.510.5, (a) Calculate the numerical value for zo(that is, z at time t = 0). Show every step of all calcu- lations. I (b) Derive the expression for the growth rate of z (denoted by g2 ) as a function of gr and gy. Show every step of all calculations. (c) Derive the expression for zt as a function of gr, gy, 20; and t. Show every step of all calcula- tions. (d) Calculate the numerical values for z5 and zio( that is, z at time t = 5 and zt at time t = 10) by using the expression that you derived in part (c). Show every step of all calculations

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