Consider the one-country model of technology and growth that was presented in Section 8.3. Suppose that L = 1, m = 10, and gA = 0.3. (These numbers are not meant to be realistic but rather are chosen to make the calculations easier. There has certainly never been a country where one third of the labor force was engaged in R&D!) Calculate the growth rate of output per worker. Now suppose that gA is raised to 0.6. How many years will it take before output per worker returns to the level it would have reached if gA had remained constant?

(Note: You can solve this problem by using a calculator or computer or by applying some of the tricks for working with growth rates discussed in Chapter 1.)