# Test Answers to an Advanced Mathematics and Earth Science Test Essay

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Question 1
A function is the mathematical way of describing a relationship between two sets of variables. In usual notation, the set of the independent variables x, is called the domain and the set of the dependent variables y is termed the range.
Most commonly encountered functions are
The linear function y = x, the quadratic function y = x2, the cubic function
y = x3, the exponential function y = ex, the logarithmic function y = log(x), and periodic functions such as y = cos x, y = sin x, the set of the variable quantity x is the domain, and the set of the corresponding values of the variable y constitutes the range.
Below I reproduce (courtesy of the mathsisfun website,
www.mathsisfun.com/sets/functions-common.html), in descending order,
cubic, logarithmic,
the sine, and the exponential functions graphs.
Question 2
Carbon dating is the method whereby the age of very old objects is estimated.
The method consists of measuring the current radioactivity of the specimen due to its unstable (and rare) carbon isotope 14C content and comparing it with the average background radioactivity of the atmosphere. (Willard Libby 1947). The specimen must contain remains of a plant. So long as the plant was alive its radioactivity due to the intake of CO2 from the atmosphere was equal to the radioactivity of the atmosphere however when it died, the amount of 14C in it began to fall due to the radioactive decay of this element into nitrogen (14N). The half-life of 14C, defined by T_(1/2)=(ln⁡(2))/λ, can be measured experimentally and is found to have the value 1.808 ×〖10〗^11 seconds. The above expression results from the fact that nuclear decay, and therefore the radioactivity of a radioactive...

... middle of paper ...

... mount Everest at 8863 m from the surface of the Earth, and using the known values of the weighted molar masses of oxygen and nitrogen, the gravitational acceleration constant, the gas constant, and assuming a temperature of 273 K (or 0 degrees Celsius), (Calter and Calter, 2011.) we obtain a pressure of about 0.034 mega pascal which is equivalent to 0.33 atmosphere which is a third of what we have at sea level.
References
1 P. Calter and M. Calter, Technical Mathematics, 6th ed. Jonh Wiley and Sons, 2011.
2 The Wolfram Functions Site,
www.functions.wolfram.com.
3 D. Halliday, R. Resnick, J. Walker, Fundamentals of Physics, John Wiley and Sons, 2005 (chapter 44).
4 Willard Libby – Noble Lecture: Radiocarbon Dating,
www.nobelprize.org/nobel_prizes/chemistry.
5 P. Schmidt and F. Ayers, Schaum’s Outline of College Mathematics, McGraw-Hill Companies, 2010.

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- Question 1 A function defines a relation between two sets of quantities in such a way that each quantity in the first set, which is called the domain, is related to a certain quantity in the second set, which is called the range. Thus in the linear function y = x, the (simplest) 3rd degree polynomial y = x3, the exponential function y = ex, and the (natural) logarithmic function y = ln(x), the set of possible values of the quantity x are the domain, and the set of the corresponding values of y are the range....   [tags: solving functions, logarithmic equations]

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