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World oil production/consumption
# oil production per day by country
production = read.csv("production.csv", header = T)
# proven oil reserves by country
reserves = read.csv("reserves.csv", header = T)
# oil consumption by country
consumption = read.csv("consumption.csv", header = T)
# the total amount of oil production per year
total_production = sum(production$Production) * 365
# total world proven reserves
total_reserves = sum(reserves$Reserves)
# total world consumption per year
total_consumption = sum(consumption$Consumption) * 365
# derivation of time formula
#
# Take the simple exponential growth function
# q is initial quantity, r is growth rate, t is time
#
# f(t) = q * exp(r * t)
#
# Total usage over time is the integral of f(t):
#
# V(T) = int(f(t), 0, T)
# = int(q * exp(r * t), 0, T)
# = q / r * (exp(r * T) - 1)
#
# See when this hits some limit L
#
# L = V(T)
# = q / r * (exp(r * T) - 1)
#
# Solve for T
#
# T = ln(L * r / q + 1) / r
# initial quantity is current production
q = total_production
# set growth rate to 1.18%
r = 0.0118
# set limit equal to current proved reserves
L = total_reserves
print(sprintf("Current reserves are %e, current consumption is %e, current production is %e.", total_reserves, total_consumption, total_production))
# this is when we will hit that limit
t = log(L * r / q + 1) / r
print(sprintf("Assuming no production growth, we will hit L in %f years.", total_reserves / total_production))
print(sprintf("Assuming a growth rate of %f%% per year, we will hit L in %f years.", round(r * 100, 2), t))
# now for consumption
q = total_consumption
t = log(L * r / q + 1) / r
print(sprintf("Assuming no consumption growth, we will hit L in %f years.", total_reserves / total_consumption))
print(sprintf("Assuming a growth rate of %f%% per year, we will hit L in %f years.", round(r * 100, 2), t))
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