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Bourne, Murray. “3. The Logarithm Laws.” Intmathcom RSS, www.intmath.com/exponential-logarithmic-functions/3-logarithm-laws.php.
This section of the investigation caused some mayhem, as I had a lot of issues within this particular area of the report. I had produced an equation and had found it difficult to solve it. 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: 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 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 verifyErrors }}{{ message }}{{ /verifyErrors }}{{
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℃. Although seemingly accurate, I wanted to further explore and delve into the actual math of Newton’s law of cooling, as stated in the introduction, which states that:
The graph thus holds a negative correlation, so logically it would mean that the power of the function must be negative. Experimentally Determined Values of the Temperature of the Coffee (℃) Over a Fixed Period of Time (Two Hours) Through a Series of Five Minutes Intervals
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.