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.
355 exam-style questions on OCR (MEI) A Level Maths 2.5 Statistical Hypothesis Testing, covering 2.5.1 Process and language of hypothesis testing, 2.5.2 When to apply 1-tail and 2-tail tests, 2.5.3 Significance level and incorrect rejection, 2.5.4 Null and alternative hypotheses (binomial), 2.5.5 Conduct a binomial hypothesis test, 2.5.6 Critical and acceptance regions (binomial), 2.5.7 Distribution of the sample mean (A-level only), 2.5.8 Hypothesis test for a single mean (A-level only), 2.5.9 Critical and acceptance regions (mean) (A-level only), 2.5.10 Correlation as closeness to a straight line (A-level only), 2.5.11 Inference using a correlation coefficient (A-level only), and 2.5 Statistical Hypothesis Testing. Each one has a worked solution and a mark scheme showing where the marks go.