This is the write-up for assignment 12.
In this write up we will be using EXCEL spreadsheet
to help in our exploration to the problem presented.
In this exploration we collected temperature data as a cup of boiling water cooled. The initial temperature was taken as soon as the water reached a boiling state (time=0). We collected data each minute of the temperature of the water as the water cooled. We did this data collection for 30 minutes.
Next, we entered this observed data in an EXCEL spreadsheet and let the software analyze the data and produce a graph of the observed data. Below is the graph that the observed data produced.
After viewing this graph, we tried to construct a function that will model this observed data.
The formula that we constructed was f(x)=93.4*EXP(-0.076958*A6)+118.6. Below is a graph of the observed data and the theorectical data from our constructed formula.
Click here to see the EXCEL file of our oberved data, theoretical data, and residuals.
Using this function we predicted what the temperature would be after 45 minutes, 60 minutes, and 300 minutes. According to our function the temperature after 45 minutes will be 121.5 ºF; after 60 it will be 119.5 ºF; and after 300 minutes 118.6 ºF.
Finally, we calculated the measure of error between our model and the observed data by taking the square of the difference for each time, sum the squares, and divided 30 (number of data collections). We used this statistic to guide us in refining our function to model the data.The function that we constructed has a measure of error between our model and the observed data of 3.70365 (the average of the sum of the squared residuals).