1.1. It is believed that the relationship between two variables, x and y, can be modelled by y = bp^x. By first taking logarithms of both sides and then by using the laws of logarithms, show that y = bp^x can be written as log y  = log b + x log p .

1.2. The scatter diagram below shows the relationship between two sets of data, x  and log y.  The regression line of log y on x  is shown and passes through the points (3, 0.7)  and  (7, 1.3).

(i) Using the given coordinates, find the gradient of the regression line shown.

(ii) Find the regression line of log y on x in the form log y = a + mx,  where a and m are constants to be found.

1.3. (i) By comparing the equations in (a) and (b)(ii) show that  b = 1.778 to three decimal places.

(ii) Find the value of p to three decimal places.