Hi, last year in grade 11, I basically failed methods PSMT, I didn't know what to do and gave up and the teachers could only give minimal assistance but I really had no clue what to do. This year, the teachers keep asking us to refer back to our last year's assignment but the thing is, its a complete disaster . So therefore, I would
really appreciate any assistance with my task this year
Basically, we were given data looking at temperature per min of the black/milk before/milk after tea and were asked to investigate the claim that the tea will not cool as quickly as if you add the milk after adding the hot water.
The topic is basically about further calculus and differentiation but my teacher has told us that we need to do linearisation which comes in two forms: semi-log and log-log (if I'm correct).
e.g. for semi log, I used the exponential equation y=Ae^kx and made it to a semi-log equation ln(y)=kx+ln(A)
If you'll have a look at the attatchment I make a graph based on the time and the log of temperature and then added the linear regression trendline which gave me a nice line of y=-0.0115x+4.2456
I then used the linear stat regression to find a k (m) and A (b) value and get the equation: y=4.2456×e^(-0.0115x) which can also be graphed against the data.
How would I know which graph to use/what determines a good graph?
Additionally, when I made a residual plot from the data, I got something like... (open attachment 2) but when I searched it up, a u-shape correlation means that a linear model is NOT fit for the graph so I'm just really confused in all
And also where does the differentiation takes place? I assume that's after I generate a good model and then differentiate it to determine the maximum?
Hope you understand what I mean and thank you so much for reading, I really appreciate it
~Jas383