EnGrowth

That Identifies the rate of growth companies Relates With expansion

Given the 1 to 1 relationship between energy expansion and GDP growth, the next identity must be met:

(1) (1+∆PIB)n=1+k

where ΔPIB is the annual growth rate of GDP, n the number of years of the period considered and k the rate of accumulated growth in the same period. Thus, for example, if it is estimated that the energy system will expand by 66% over a 23-year horizon, with these data the average annual growth rate of GDP can be calculated substituting the corresponding values in equation (1) ; that is to say:

(2) (1+∆PIB)23=1.66.

Applying a logarithmic identity on both sides of the previous equation, results:

(3) 23 Ln(1+∆PIB) = Ln(1.66). So:

(4) Ln(1+∆PIB) = (Ln(1.66))/23.

To clear ΔPIB it is necessary to apply the inverse of the neperian logarithmic function, that is, the Euler exponential, so that:

(5) e^(Ln(1+∆PIB) ) = e^((Ln(1.66))/23)

implies that:

(6) 1+∆PIB = e^((Ln(1.5))/23),

and in consequence:

(7) ∆PIB = e^((Ln(1.66))/23) – 1

The formula (7) allows to calculate the limit of growth of the GDP in function of the expansion of the energetic production; it is applicable for any time horizon and expansion goal.