A common pattern in long-term metals production

A common pattern equation for the production of metals over their entire life is proposed. The equation is tested for five metals namely: copper, aluminum, lead, molybdenum and tungsten which have distinctly different historical spans. Various stages of early and take-off growth are identified and labeled stages I-IV. The very early stage of growth leading to a diminishing in activity appears to be decoupled from the later high growth stages. An approximately 12 year perturbation life cycle is noted in stage III for most metals. Copper and aluminum are not yet in stage IV, nor show any signs of entering this stage in the next 50 years. The pattern equation appears to have generality. A strict interpretation of the various parameters in the pattern equation is not attempted in this article.