The population of a specific bacteria colony ( $N$ ) recorded $h\,$ hours after an experiment began is shown in the table below.


$h$	1	2	4	7	10	12
$N$	190	290	660	2300	7900	18000

The data is coded using the changes of variable $x = h$ and $y = \log_{10} N$ .

The regression line of $y\,$ on $x\,$ is found to be $y = 2.10 + 0.18 x$ .

Given that the data can be modelled by an equation in the form $N = ab^h$ where $a\,$ and $b\,$ are constants, find the values of $a\,$ and $b\,$ to 3 significant figures.

Give an interpretation of the constant $a\,$ in this equation.

Explain why this model might not be reliable for predicting the population after 1 week.

The population of a specific bacteria colony ( $N$ ) recorded $h\,$ hours after an experiment began is shown in the table below.


$h$	1	2	4	7	10	12
$N$	190	290	660	2300	7900	18000

The data is coded using the changes of variable $x = h$ and $y = \log_{10} N$ .

The regression line of $y\,$ on $x\,$ is found to be $y = 2.10 + 0.18 x$ .

Given that the data can be modelled by an equation in the form $N = ab^h$ where $a\,$ and $b\,$ are constants, find the values of $a\,$ and $b\,$ to 3 significant figures.

Give an interpretation of the constant $a\,$ in this equation.

Explain why this model might not be reliable for predicting the population after 1 week.

1.6 Exponentials and logarithms

Question 3

Markscheme

1.6 Exponentials and logarithms

Question 3

Markscheme

1.6 Exponentials and logarithms

Question 3

1.6 Exponentials and logarithms Questions

1.6 Exponentials and logarithms

Question 3

1.6 Exponentials and logarithms Questions