1. a population with an annual growth rate of 3% doubles roughly every years. 2. a population with an annual growth rate of 4% doubles roughly every years. 3. a population with an annual growth rate of 7% doubles roughly every years. 4. a population that doubles in size every 14 years has a growth rate of percent. 5. a population that doubles in size every 35 years has a growth rate of percent.

(30 total points) suppose a firm’s production function is given by q = l1/2*k1/2. the marginal product of labor and the marginal product of capital are given by: mpl = 1/ 2 1/ 2 2l k , and mpk = 1/ 2 1/ 2 2k l . a) (12 points) if the price of labor is w = 48, and the price of capital is r = 12, how much labor and capital should the firm hire in order to minimize the cost of production if the firm wants to produce output q = 18?