EnGrowth APK

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

(1) (1 + ΔPIB) n = 1 + k

ΔPIB Where 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 the average These data annual growth rate of GDP can be Calculated Substituting the Corresponding values ​​in equation (1); That is to say:
(2) (1 + ΔPIB) 23 = 1.66.

Applying a logarithmic identity on Both Sides of the previous equation, results:

(3) 23 Ln (1 + ΔPIB) = Ln (1.66). SW:

(4) Ln (1 + ΔPIB) = (Ln (1.66)) / 23.

To clear ΔPIB it is Necessary to apply the inverse of the logarithmic function neperian, That is, the Euler exponential, so that:
(5) e ^ (Ln (1 + ΔPIB)) = e ^ ((Ln (1.66)) / 23)
IMPLIES that:
(6) 1 + ΔPIB = e ^ ((Ln (1.5)) / 23),
and in consequence:
(7) ΔPIB = 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.