The population of a specific bacteria colony (NNN) recorded h h\,h hours after an experiment began is shown in the table below.
| hhh | 1 | 2 | 4 | 7 | 10 | 12 |
| NNN | 190 | 290 | 660 | 2300 | 7900 | 18000 |
The data is coded using the changes of variable x=hx = hx=h and y=log10Ny = \log_{10} Ny=log10N.
The regression line of y y\,y on x x\,x is found to be y=2.10+0.18xy = 2.10 + 0.18xy=2.10+0.18x.
Given that the data can be modelled by an equation in the form N=abhN = ab^hN=abh where a a\,a and b b\,b are constants, find the values of a a\,a and b b\,b to 3 significant figures.
Give an interpretation of the constant a a\,a in this equation.
Explain why this model might not be reliable for predicting the population after 1 week.
278 exam-style questions on CCEA A Level Maths 2.5 Data presentation and interpretation, covering 2.5.1 Data presentation and interpretation, 2.5.2 Data presentation and interpretation, 2.5.3 Data presentation and interpretation, 2.5.4 Data presentation and interpretation, 2.5.5 Data presentation and interpretation, 2.5.6 Data presentation and interpretation, 2.5.7 Data presentation and interpretation, 2.5.8 Data presentation and interpretation, 2.5.9 Data presentation and interpretation, and 2.5 Data presentation and interpretation. Each one has a worked solution and a mark scheme showing where the marks go.