The graph thus holds a negative correlation, so logically it would mean that the power of the function must be negative. To translate this equation to represent the original, it requires a translation on the x axis (k) and a gradient much smaller 1(a), so it can be assumed that: The line, as depicted through the graph, can be seen to be accounted for small uncertainties in the line created by real world factors. The equation for the line of best fit was generated:

However, with the equation produced above, despite the discrepancies, it represents an extremely accurate model of the cooling coffee. Thus I have fulfilled my objective of determining an equation to model the cup of cooling coffee through implementing the laws of logarithms and simultaneous equations. Through this investigation, I was able to apply math to a real life situation outside of the classroom environment. is always equal to 24.5, there could have been major inaccuracies as as the coffee cooled down, the air surrounding it would have immediately warmed up as the heat diffused away from the cup (Murray, 2012). This then explains why the differences of the first and third equation were so great, as between the two, a lower ambient temperature was always predicted, thus inaccurately assuming that the rate of change was faster. Our academic experts are ready and waiting to assist with any writing project you may have. From simple essay plans, through to full dissertations, you can guarantee we have a service perfectly matched to your needs. View our services Feldman, Joel, et al. “CLP-1 Differential Calculus.” Plimpton 322, www.math.ubc.ca/~CLP/CLP1/clp_1_dc/sec_newtonCooling.html. After the data was collected in the tables and averaged out between each trial, as shown above, the next stage logically was to graph the results and produce a graph of my own. The scatter plot below was produced using Microsoft Excel, with the time in minutes (over 5 minute intervals) – in the graph the scale was deduced to 20 minute intervals - plotted on the X axis and the temperature (℃) plotted on the Y axis. The graph below thus indicates the experimentally determined values of the temperature of the coffee over a series of two hours (with the result

How we tested

is directly proportional to the difference between the temperature of the soup T(t) and the ambient temperature Tc . Experimentally Determined Values of the Temperature of the Coffee (℃) Over a Fixed Period of Time (Two Hours) Through a Series of Five Minutes Intervals As indicated through the graph, the two lines are basically identical, and the equation produced greatly resembles the first equation produced. Figure 1.7: Original data compared to T ( t ) = 24 + ( 55 . 9 ) e – 0 . 0279 t

To answer my original research question, “How long can I revisit my coffee before it becomes undrinkable?”, I can achieve this by using the second equation: Bourne, Murray. “3. The Logarithm Laws.” Intmathcom RSS, www.intmath.com/exponential-logarithmic-functions/3-logarithm-laws.php. If you need assistance with writing your essay, our professional essay writing service is here to help! Essay Writing ServiceAccording to online publications, integration was used through Newton’s law of cooling, and the fact that