Question

Given the rate of investment is I(t)=2 t^1/3,where 't' is time.Suppose the initial capital stock K is 25. Find the amount of capital accumulation during the time intervals [0,1] and [1,3].

Answer 1

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Answer 2

In this question we will apply the concept of integration as follows :

K∫l(t) dt

K∫2t^1/3 dt

= 2K∫t^1/3

= 2K[3/4t^4/3]

We need the intervals [0,1] and [1,3]

[0,1]

25 × 2{ [3/4 × 1^4/3] - [3/4 × 0^4/3]}

50(3/4 - 0)

= 37.5

[1,3]

50{[3/4 × 3^4/3] - [3/4 × 1^4/3]}

50{ 3.245 - 3/4}

= 50 × 2.495

= 124.75