A collector tracks the value of a vintage guitar over 10 years. The time, xxx (years), and the value, yyy (in £1000s), are recorded in the table below.
| xxx | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| yyy | 8.5 | 10.2 | 12.8 | 15.5 | 18.9 | 23.1 | 28.4 | 34.2 | 41.5 | 50.8 |
The data is coded using the changes of variable r=xr = xr=x and s=log10ys = \log_{10} ys=log10y.
The product moment correlation coefficient for the coded data is 0.97. Comment on r r\,r for this model and therefore justify the use of a model in the form y=abxy = ab^xy=abx where a a\,a and b b\,b are constants.
The regression line of s s\,s on r r\,r is found to be s=0.840+0.086rs = 0.840 + 0.086rs=0.840+0.086r.
Find the values of a a\,a and bbb, give your answers to 3 significant figures.
104 exam-style questions on WJEC A Level Maths 1.6 Exponentials and logarithms, covering 1.6.1 Exponentials and logarithms, 1.6.2 Exponentials and logarithms, 1.6.3 Exponentials and logarithms, 1.6.4 Exponentials and logarithms, 1.6.5 Exponentials and logarithms, 1.6.6 Exponentials and logarithms, 1.6.7 Exponentials and logarithms, 1.6.8 Exponentials and logarithms, and 1.6.9 Exponentials and logarithms. Each one has a worked solution and a mark scheme showing where the marks go.