It is reasonable to say that Humans have not been around for 200,000 years

Argument: The Math The rate of change in any population can be calculated only with data. For instance, in the United States, the Bureau of the Census acquires population data over a period of time and reports statistical studies performed on that data. A rate of change is generally linear because the rate is based on averages. It is a quantitative calculation as opposed to a qualitative calculation. For instance, the rate of population growth in the United States between the years 1990, population 248.7 and 2000, population 281.4, is calculated as: Rate = (281.4-248.7) / 10 = 327,000 per year But we know that it is highly unlikely that exactly 327,000 people were added to the population every year for ten years. The probability is that the population varied by larger or smaller amounts year over year. This holds especially true when attempting to calculate population growth from prehistory through the present time. First, in order to do a calculation, data is required. The first census in the United States was in 1790. There are no prehistorical records or estimates of populations across the globe. Even if a few records existed, it would be impossible to determine the rate of growth of the entire Earth based on a few populations out of thousands of populations that existed at the time. Second, the rate of change is a statistical calculation. Anomalies like mass extinctions are not taken into account. We know from the fossil record that catastrophic events occurred since the first human walked on the Earth. In fact, a recent study found just such evidence for the end-Triassic extinction, caused by a series of massive eruptions in north-central Pangaea, and recently completed studies into the Chicxulub impact all but confirm that a massive impactor was indeed responsible for the extinction of the dinosaurs. But what about humans? There is one near-extinction event that is fairly well-known, although it remains controversial. Roughly 70,000 years ago, give or take a few thousand years, an enormous eruption occurred in what is now Sumatra, leaving behind Lake Toba . The eruption coincides with a population bottleneck that is often cited as the reason for the relatively low genetic diversity across Homo sapiens sapiens. Research suggests as few as 2,000 humans were left alive by the eruption and its aftereffects. Catastrophic events have even altered the population growth rate as recently as the early 1900's after the First World War. There were so many casualties relative to the total population of the Earth that the growth rate of the entire globe was impacted. The Fossil Record The fossil record shows that humans have been around for approximately 200,000 years. This data is derived from physics. There are two types of dating methods: absolute and relative. Absolute dating methods include radiometric methods such as Postassium-Argon and Rubidium-Strontium. The data derived from radiometric dating gives specific time frames in the Earth's history when the human fossil was likely to live. Relative dating methods include analysis of strata (layers) of rock. A fossil found in a particular strata can be dated by correlation. One of the most recent advances in fossil dating is magnetic orientation. The magnetic poles in material can be associated with a particular time in Earth's history when the poles might have been in a different position. Pottery in particular can be dated quite accurately using the magnetic pole orientation method. In conclusion, the combination of simple mathematical functions like rate of change in two variables and modern physics offers a massive amount of hard evidence that humans have occupied the Earth for at least 200,000 years.