Consider the endogenous growth model AK, in which the production function is given by Y = AK. Suppose s denotes the saving rate; that δ represents the depreciation rate; and that the variable that represents the population and that grows at the rate n. Calculate the growth rate of capital per capita in the same way as for the Solow model and, from there, solve the differential equation to obtain the capital per capita (denoted by k) as a function of time.

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A: Amount of labor (L) = 1000Investment rate (s) = 0.1Depreciation rate (d) = 0.4Productivity (A) = 1