The book is divided into chapters, most of which are simply collections of journal articles on a common topic. An exception is the first chapter, in which Bartlett recounts the history of the talk and his subsequent research on exponential arithmetic. Chapter Two contains six articles on the energy crisis spanning the years 1976–2001 in which Bartlett argues that the public has been given overly optimistic estimates of lifetimes for fossil fuels. One such estimate, for example, states that at current levels of output and recovery U.S. coal reserves can be expected to last for more than 500 years. What Bartlett points out is that even modest growth in the consumption of coal drastically reduces the expected lifetime. At 1976 levels of consumption Bartlett estimates that U.S. coal will indeed last between 780 and 2980 years. But if consumption grows at an annual rate of 3 percent, then the estimates fall to between 105 and 149 years. If the growth rate is 10 percent, the estimates fall to between 43 and 57 years. Bartlett rightly criticizes leaders from government and industry who promulgate optimistic lifetimes “at current rates of consumption” while at the same time pressing for increased reliance on coal.

Bartlett builds on the work of M. King Hubbert, who empirically modeled the full life cycle of the production of non-renewable resources. In this analysis, per-year production tends to follow a Gaussian curve, growing from year to year, peaking at some point, and then declining eventually toward zero annual production. U.S. oil production peaked in 1970, and in a 2000 study Bartlett estimated that it will decline to one-third of the peak value by 2020. World oil production is projected to peak some time between 2004 and 2030.

Chapter Three contains four articles on population growth, which in Bartlett’s view is the root of most of the world’s problems, the energy crisis among them. Bartlett repudiates the popular view that overpopulation is mostly a problem for the third world. In his view, the U.S. consumes the lion’s share of the world’s finite resources and zero growth in the U.S. population is an absolute requirement if the future is to look anything other than dismal. In order to achieve this goal we would have to allow no immigration into the U.S. and reduce the birth rate to 59% of its 1992 value. Some immigration could be allowed if the birth rate fell to even lower values. The argument against immigration seems overly simplistic; does a middle-class European automatically become more wasteful when he crosses the pond? Does a citizen of the U.S. acquire a social conscience when she emigrates to Australia? The argument for reduced birth rate would call for a voluntary or mandatory limit of approximately one child per married couple. Since the zero-population-growth argument is founded on the assumption of a fundamentally prodigal American character, neither voluntary nor mandatory limits would seem to be on the horizon.

The final article of Chapter Three, “The Massive Movement to Marginalize the Modern Malthusian Message”, is an elaborate attempt to classify and categorize those who do not agree that population growth is the most pressing concern of the planet. Briefly, Believers are the good guys, those who agree with Bartlett. Critics can be divided into Non-Believers (who, according to the article, are probably innumerate) and Diverters (who know the Truth but who, for a variety of reasons, try to convince others of its falsity). The tone of the article is less than charitable and might come off as a rant to readers who are not already Believers.

One of Bartlett’s pet peeves is the oxymoronic term “sustainable growth”. The four articles of Chapter Four deal with applications and misapplications of the term “sustainable” as applied to problems of population and finite resources. The first article advocates a program for “sustained availability,” in which the rate of extraction of a resource declines each year at such a rate that the resource lasts “forever”. While this is an interesting mathematical puzzle, the result does not seem to be fundamentally different from that which would come about in a laissez-faire approach. In the “sustained availability” future some kind of central planning authority decreases the extraction quota each year according to a mathematical projection. In the laissez-faire future, it becomes increasingly expensive to extract the dwindling resource until it is no longer economical to do so on the same scale as previously. In neither future does the extraction rate necessarily fall to zero, and in both futures the population must make do with an extraction rate significantly less than the historical peak.

Chapter Five contains an article by M. King Hubbert, whose Gaussian model for resource depletion appears in many of Bartlett’s articles. One article by physicist David Roper provides a theoretical foundation for Hubbert’s empirical observation. Another Roper article applies this theory to U.S. petroleum and natural gas depletion. Roper’s model allows for an asymmetric extraction curve in which the decline in the extraction rate is not necessarily as rapid as the rise leading up to the peak. This means that the modeled resource may last somewhat longer than would be predicted by the Gaussian model. The end of the story is the same, nevertheless; the resource is extracted at miniscule rates in the distant future.

Chapter Six consists of three articles previously published in Population & Environment. The first outlines the principles of discrete and continuous compounding, describes the use of logarithmic scales for plotting data, and gives methods for calculating doubling times. The second article is built around the example from Life magazine of a 98-year-old man who had 200 great-grandchildren and goes on to develop mathematical models for determining the number of children, grandchildren, and great-grandchildren who would descend from a hypothetical person under various scenarios. The third article in the series compares the growth in profits and wages from 1989 to 1997. Bartlett concludes that corporate profits grew 25 times as fast as wages during this time period.

Chapter Seven consists of 14 articles written for The Physics Teacher between 1976 and 1998 that develop the mathematics of the exponential function and apply it to a variety of real-world problems, including compound interest, inflation, highway construction, population growth, postage rates, gasoline shortages, and curve fitting. The material from Chapters Six and Seven are among the most timeless in the book, applying exponential arithmetic to a variety of model problems that are not necessarily tied to particular political and economic messages.

Chapter Eight consists of endnotes by Robert Fuller, Vicki Clark, and John Rogers, who convinced Bartlett that The Essential Exponential deserved to be archived in book form for the use of planet-conscious science teachers. Chapter Nine is an annotated bibliography of articles by Bartlett.

I suspect that The Essential Exponential will not be well-received by Non-Believers and Diverters. Bartlett is not shy about expressing his disdain for “experts” who disagree with his political and economic messages (p 98):

There seems to be a concerted effort, locally, nationally, and globally to marginalize the modern Malthusian message and to talk about sustainability, using terms and concepts which don’t offend anyone. This marginalization requires that we make no mention of the facts that at all levels,

(a) Sustainability requires that both population and the rates of consumption of resources be stabilized at levels substantially smaller than those of today and,

(b) The world’s worst population problem is right here in the U.S.

Believers will appreciate these messages and admire Bartlett’s tenacity in fighting the good fight for more than three decades. Scientists of all political stripes, however, should applaud him for bringing to these politically and emotionally charged debates the underlying central message that mathematics is the language best suited to exploring issues in which numbers really count.