A scientist measures the growth of a bacterial colony over 10 days. The time, ttt (days), and the number of bacteria, NNN, are recorded and the results are shown in the table below.
| ttt | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| NNN | 45 | 72 | 124 | 190 | 321 | 512 | 830 | 1345 | 2150 | 3500 |
The data is coded using the changes of variable r=tr = tr=t and s=log10Ns = \log_{10} Ns=log10N.
The product moment correlation coefficient for the coded data is 0.99. Comment on r r\,r for this model and therefore justify the use of a model in the form N=abtN = ab^tN=abt 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=1.45+0.210rs = 1.45 + 0.210rs=1.45+0.210r.
Find the values of a a\,a and bbb, give your answers to 3 significant figures.