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The final equation produced seems to produce a graph that matches the original data, but it can be seen with the results that the rate of cooling in the first 50 seconds of cooling is underpredicted. 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: As can be seen in the above figure, the graph shows an exponential curve, between the values of temperature of the coffee and the time in minutes.
Figure 1.6: Graph displaying the original data versus the original data graphed according to the equation T = 24 . 5 + 54 . 5 e – 0 . 0274 t If you need assistance with writing your essay, our professional essay writing service is here to help! Essay Writing Service
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Feldman, Joel, et al. “CLP-1 Differential Calculus.” Plimpton 322, www.math.ubc.ca/~CLP/CLP1/clp_1_dc/sec_newtonCooling.html. is directly proportional to the difference between the temperature of the soup T(t) and the ambient temperature Tc . 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. As can be seen below, the data are basically identical, with the only difference being that the equation generated values intersect the y-axis at a lower value. The asymptote is the same, with the mean error of the differences in values being 0.11℃. I can safely revise that 1.41 hours will be the proper time before my coffee is undrinkable. As precise as this value is however, it only represents how long I can leave my coffee out in a room with 24℃ temperature. A second investigation would be interesting to see if an equation could be produced that takes into account the surface area of the cooling body and the changing ambient temperature.
Due to the temperature of the room being 24℃, the entire graph was translated up the y axis by a degree of 24, and thus there was a translation constant: It can be seen from the graph that the actual data (orange) tends to be slightly lower than the temperature projected by the original data. I believe that this could It can be seen that the second equation, which was produced using lines of best fit, produced the most accurate model of the coffee cooling down.This is most likely due to the fact that the lines of best fit take into account the slight discrepancies in the real results that were caused by the environment. Since the third and first equation rely on the fact that 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. and 35.4 degrees. I then used two results from the data to create a pair of two variable equations whereThe 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:
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