An urban planner monitors the population growth of a developing city over 10 decades. The number of decades, $x$ , and the population in thousands, $y$ , are recorded in the table below.


$x$	1	2	3	4	5	6	7	8	9	10
$y$	18	26	38	55	78	112	158	225	321	460

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

The product moment correlation coefficient for the coded data is 0.998. Comment on $r\,$ for this model and therefore justify the use of a model in the form $y = ab^x$ where $a\,$ and $b\,$ are constants.

The regression line of $s\,$ on $r\,$ is found to be $s = 1.12 + 0.155 r$ .

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

An urban planner monitors the population growth of a developing city over 10 decades. The number of decades, $x$ , and the population in thousands, $y$ , are recorded in the table below.


$x$	1	2	3	4	5	6	7	8	9	10
$y$	18	26	38	55	78	112	158	225	321	460

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

The regression line of $s\,$ on $r\,$ is found to be $s = 1.12 + 0.155 r$ .

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

1.6 Exponentials and logarithms

Question 5

Markscheme

1.6 Exponentials and logarithms

Question 5

Markscheme

1.6 Exponentials and logarithms

Question 5

1.6 Exponentials and logarithms Questions

1.6 Exponentials and logarithms

Question 5

1.6 Exponentials and logarithms Questions