Here's something I need explaining. I found this formulae in a spreadsheet. And this example. I cannot figure out how it works. I plug in the numbers and I don't get 342, but that's the answer given by the PHD Al Bartlett, so he cannot be wrong. Can someone explain what are the values he uses for k and r please. R clearly must equal 6.81 x 10^21 barrels
The volume of the earth is 6.81 x 10^21 barrels, which would last for 4.1 x 10^11 yr if the 1970 rate of consumption of oil held constant with no growth. The use of Eq. (6) shows that if the rate of consumption of petroleum continued on the growth curve of 7.04 % / yr of Fig. 2, this earth full of oil will last only 342 yr!
T = ( 1 / k ) ln ( k R / r + 1 )
where r is the current rate of consumption at t = 0, e is the base of natural logarithms, k is the fractional growth per year, and t is the time in years, and size of the resource is R
The volume of the earth is 6.81 x 10^21 barrels, which would last for 4.1 x 10^11 yr if the 1970 rate of consumption of oil held constant with no growth. The use of Eq. (6) shows that if the rate of consumption of petroleum continued on the growth curve of 7.04 % / yr of Fig. 2, this earth full of oil will last only 342 yr!
T = ( 1 / k ) ln ( k R / r + 1 )
where r is the current rate of consumption at t = 0, e is the base of natural logarithms, k is the fractional growth per year, and t is the time in years, and size of the resource is R
