Question

The table shows the temperature of an amount of water set on a stove to boil, recorded every half minute.According to the line of best fit, at what time will the temperature reach 100°C, the boiling point of water?55.566.5

Answer 1

This is a problem with a non-linear equation. The data is the temperature of water and the time. But we have to fit a line anyway.

We can the Least Squares Method, the best line fit is:

`\begin{gathered} y=mx+b \\ m=\frac{n\sum ^{}_{}(x\cdot y)-\sum ^{}_{}x\cdot\sum ^{}_{}y}{n\sum ^{}_{}x^2-(\sum ^{}_{}x)^2} \\ b=\frac{\sum ^{}_{}y-m\sum ^{}_{}x}{n} \\ \text{where n is the number of points} \end{gathered}`

Now, we apply the formula above:

`m=(10\cdot2072.5-22.5\cdot880)/(10\cdot71.25-22.5^2)=(20725-19800)/(712.5-506.25)=(925)/(206.25)=4.48`