The value of a particular model of car, £V\pounds V£V, when it is t t\,t years old is modelled by
V=abtV = ab^{t}V=abt
where a a\,a and b b\,b are constants.
A dealer records the value of a number of these cars of different ages. The data are coded using y=log10Vy = \log_{10} Vy=log10V, and the regression line of y y\,y on t t\,t is found to be
y=4.28−0.0862ty = 4.28 - 0.0862ty=4.28−0.0862t
Express V V\,V in the form Ae−ktAe^{-kt}Ae−kt, where A A\,A and k k\,k are positive constants. Give the values of A A\,A and k k\,k to 3 significant figures.
Using this model, find how long it takes for the value of one of these cars to fall to one third of its value when new. Give your answer to the nearest month.
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.