.Capital formation is the process of adding to a given stock of capital. Regarding this process as continuous over time, we may express capital formation as a function of time, C(t), and use the derivative dC/dt to denote the rate of capital formation.
The rate of capital formation at time t is identical with the rate of net investment flow at time t, denoted by I(t).
Thus, capital stock C and net investment I are related by:
(1)
dC
dt
= 1(t)
Identity (1) shows the synonymity between net investment and the increment of capital.
Suppose thatI(t) = 6 x √√6t + 0.06and that the initial stock of capital at time zero is C(0)=36. Use Identity (1) to set up and solve an indefinite integral in order to determine the capital formation function C(t) for the given I(t).