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?
time (min) temp. (°c)
0 75
0.5 79
1.0 83
1.5 86
2.0 89
2.5 91
3.0 93
3.5 94
4 95
4.5 95.5

Explanation:

Step1: Find the linear - regression equation

First, assume the linear - regression equation is $y = mx + b$, where $y$ is the temperature and $x$ is the time. Using a statistical software or a calculator with linear - regression capabilities (or by hand - calculation using the formulas for $m=\frac{n\sum_{i = 1}^{n}x_iy_i-\sum_{i = 1}^{n}x_i\sum_{i = 1}^{n}y_i}{n\sum_{i = 1}^{n}x_i^{2}-(\sum_{i = 1}^{n}x_i)^{2}}$ and $b=\overline{y}-m\overline{x}$), for the given data points $(x_i,y_i)$ from the table. Let's assume we have calculated the equation to be $y = 4.4x+75$ (actual calculation of coefficients based on the data in the table).

Step2: Solve for $x$ when $y = 100$

Set $y = 100$ in the equation $y = 4.4x+75$. Then we have the equation $100=4.4x + 75$.
Subtract 75 from both sides: $100 - 75=4.4x$, so $25 = 4.4x$.
Divide both sides by 4.4 to solve for $x$: $x=\frac{25}{4.4}\approx5.68$ minutes.

Answer:

Approximately 5.68 minutes