question 1 is the screenshot below question is about growth rates

1. (5 points) At time t 0, a rm has an initial stock K(0) of physical capital to use in its production. Unfortunately, this physical capital breaks down over time. By time t, the initial capital stock K(0) has fallen to K(t) = K(0)e_'\" in which d is the rate at which capital deteriorates. (We'll assume that d > 0 and you should note the minus sign in front of d.) The production function specifying how the firm's output Q(t) varies with the amount of labor and physical capital is Q(t) = LU)" K0)" (a) Assume that the growth rate of the labor force L(t) is rL. Please nd the rate of growth of total output Q(t) . Give your solution in terms of symbols. (The symbols entering this problem are the constants d, K(0), a, b, and 11.) Please take care to explain all steps of your work. (b) Suppose that d = 0.02, a = 0.6, b = 0.4, and 11 = 0.04. Find a numerical solution for the rate of growth of total output. Explain your work