Question 1A function is the mathematical way of describing a relationship between two sets of variables. In usual notation, the set of independent variables x is called domain and the set of dependent variables y is called range. The most commonly encountered functions are the linear function y = x, the quadratic function y = x2, the cubic function = 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 constitute the range. Below, I reproduce (courtesy of the mathsisfun site, www.mathsisfun.com/sets/functions-common.html), in descending order, the linear, the quadratic, the cubic, the logarithmic, the sine and graphs of exponential functions.Question 2Carbon dating is the method by which the age of very old objects is estimated.The method involves measuring the current radioactivity of the specimen due to its unstable (and rare) isotope content of carbon 14C and compare it with the average background radioactivity of the atmosphere. (Willard Libby 1947). The specimen must contain remains of a plant. As long as the plant was alive, its radioactivity due to the absorption of CO2 from the atmosphere was equal to the radioactivity of the atmosphere. However, when she died, the amount of 14C she contained began to decrease 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 the nuclear decay, and therefore the radioactivity of a radioactive body...... middle of paper ...... Mount Everest at 8863 m from the Earth's surface , 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 approximately 0.034 mega pascal. which is equivalent to 0.33 atmospheres, or a third of what we have at sea level. References1 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.