The temperature of water (w∘Cw^\circ\text{C}w∘C) in a kettle t t\,t minutes after it was boiled is recorded in the table below
| ttt | 1 | 3 | 6 | 9 | 11 | 15 | 20 |
| www | 92 | 76 | 65 | 50 | 46 | 33 | 25 |
The data is coded using the changes of variable x=tx = tx=t and y=log10wy = \log_{10} wy=log10w
The regression line of x x\,x on y y\,y is found to be y=1.99−0.031xy = 1.99 - 0.031xy=1.99−0.031x
Given that the data can be modelled by an equation in the form w=abtw = ab^tw=abt where a a\,a and b b\,b are constants. Find the values of a a\,a and b b\,b to 3 significant figures.
Give an interpretation of the constant a a\,a in this equation.
Explain why this model is not reliable for calculating the temperature after 1 hour.
278 exam-style questions on CCEA A Level Maths 2.5 Data presentation and interpretation, covering 2.5.1 Data presentation and interpretation, 2.5.2 Data presentation and interpretation, 2.5.3 Data presentation and interpretation, 2.5.4 Data presentation and interpretation, 2.5.5 Data presentation and interpretation, 2.5.6 Data presentation and interpretation, 2.5.7 Data presentation and interpretation, 2.5.8 Data presentation and interpretation, 2.5.9 Data presentation and interpretation, and 2.5 Data presentation and interpretation. Each one has a worked solution and a mark scheme showing where the marks go.