Question

the table shows the temperature of an amount of water set on a stove to boil, recorded every half minute. waiting for water to boil according to the line of best fit, at what time will the temperature reach 100°c, the boiling point of water? 5 5.5 6 6.5

Explanation:

Step1: Calculate the rate of temperature increase

From \(t = 0\) (\(T=75^{\circ}C\)) to \(t = 4.5\) (\(T = 95.5^{\circ}C\)). The change in temperature \(\Delta T=95.5 - 75=20.5^{\circ}C\), and the change in time \(\Delta t = 4.5\) minutes. The rate of change \(m=\frac{\Delta T}{\Delta t}=\frac{20.5}{4.5}\approx4.56^{\circ}C\) per minute.

Step2: Use the linear - equation \(T=mt + b\) (where \(b = 75\) (initial temperature when \(t = 0\)))

We want to find \(t\) when \(T = 100\). So, \(100=4.56t+75\).
Subtract 75 from both sides: \(100 - 75=4.56t\), i.e., \(25 = 4.56t\).
Then \(t=\frac{25}{4.56}\approx5.5\) minutes.

Answer:

5.5