Suppose a: grows at a constant rate 9: = 5 percent per year. Similarly, suppose y grows at a constant rate 9,, = 1 percent per year. Suppose the value for It at time t = U is equal to 3 (that is, ID = 3), and that the value for y, at time t = 0 is equal to 2 {that is, yo = 2). Finally, suppose 21 = g'5yg'5. (a) Calculate the numerical value for 2.0 [that is, 3; at time t = 0). Show every step of all calculations. (b) Derive the expression for the growth rate of 2; {denoted by 92) as a function of 9,, and gy. Show every step of all calculations. (c) Derive the expression for 2; as a function of 91, gy, 2:0, and t. Show every step of all calcula- tions. (d) Calculate the numerical for Z5 and 21.] (that is, zt at time t = 5 and at time t = 10) by using the expression that you derived in part (c). Show every step of all calculations