An urban planner monitors the population growth of a developing city over 10 decades. The number of decades, xxx, and the population in thousands, yyy, are recorded in the table below.
| xxx | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| yyy | 18 | 26 | 38 | 55 | 78 | 112 | 158 | 225 | 321 | 460 |
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 0.998. 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=1.12+0.155rs = 1.12 + 0.155rs=1.12+0.155r.
Find the values of a a\,a and bbb, give your answers to 3 significant figures.