The temperature difference, θ ∘C\theta\,^{\circ}\text{C}θ∘C, between a heated metal block and its surroundings is recorded t t\,t minutes after cooling begins.
The data are coded using the changes of variable x=tx=tx=t and y=log10θy=\log_{10}\thetay=log10θ.
The regression line of y y\,y on x x\,x is found to be
y=1.60−0.040xy = 1.60 - 0.040xy=1.60−0.040x
Express θ \theta\,θ in the form abtab^tabt, where a a\,a and b b\,b are constants. Give the values of a a\,a and b b\,b to 3 significant figures.
Use the model to find the temperature difference after 15 minutes.
121 exam-style questions on OCR A Level Maths 2.2 Data Presentation and Interpretation, covering 2.2.1 Tables and diagrams for single variable data, 2.2.2 Area in a histogram, 2.2.3 Scatter diagrams and regression lines, 2.2.4 Informal interpretation of correlation, 2.2.5 Correlation and causation, 2.2.6 Measures of average and spread, 2.2.7 Calculations of mean and standard deviation, 2.2.8 Outliers, 2.2.9 Selecting or critiquing data presentation, and 2.2.10 Cleaning data. Each one has a worked solution and a mark scheme showing where the marks go.