A scientist measures the growth of a bacterial colony over 10 days. The time, $t$ (days), and the number of bacteria, $N$ , are recorded and the results are shown in the table below.


$t$	1	2	3	4	5	6	7	8	9	10
$N$	45	72	124	190	321	512	830	1345	2150	3500

The data is coded using the changes of variable $r = t$ and $s = \log_{10} N$ .

The product moment correlation coefficient for the coded data is 0.99. Comment on $r\,$ for this model and therefore justify the use of a model in the form $N = ab^t$ where $a\,$ and $b\,$ are constants.

The regression line of $s\,$ on $r\,$ is found to be $s = 1.45 + 0.210 r$ .

Find the values of $a\,$ and $b$ , give your answers to 3 significant figures.

A scientist measures the growth of a bacterial colony over 10 days. The time, $t$ (days), and the number of bacteria, $N$ , are recorded and the results are shown in the table below.


$t$	1	2	3	4	5	6	7	8	9	10
$N$	45	72	124	190	321	512	830	1345	2150	3500

The data is coded using the changes of variable $r = t$ and $s = \log_{10} N$ .

The regression line of $s\,$ on $r\,$ is found to be $s = 1.45 + 0.210 r$ .

Find the values of $a\,$ and $b$ , give your answers to 3 significant figures.

1.6 Exponentials and logarithms

Question 1

Markscheme

1.6 Exponentials and logarithms

Question 1

Markscheme

1.6 Exponentials and logarithms

Question 1

1.6 Exponentials and logarithms Questions

1.6 Exponentials and logarithms

Question 1

1.6 Exponentials and logarithms Questions