**??? - 2014 JUNE Q13**

The thickness of a glacier has been measured every five years from 1960 to 2010.
The table shows the reduction in thickness from its measurement in 1960.

An exponential model may be used for these data, assuming that the relationship between

(i) Show that this relationship may be expressed in the form log

(ii) Complete the table of values in the answer book, giving your answers correct to 2 decimal places, and plot the graph of log

(iii) Use your graph to find

(iv) Calculate by how much the glacier will reduce in thickness between 2010 and 2020, according to the model. [2]

(v) Give one reason why this model will not be suitable in the long term. [1]

*h*and*t*is of the form*h*=*a*x 10^{bt}, where*a*and*b*are constants to be determined.(i) Show that this relationship may be expressed in the form log

_{10}*h*=*mt*+*c*, stating the values of*m*and*c*in terms of*a*and*b*. [2](ii) Complete the table of values in the answer book, giving your answers correct to 2 decimal places, and plot the graph of log

_{10}*h*against*t*, drawing by eye a line of best fit. [4](iii) Use your graph to find

*h*in terms of*t*for this model. [4](iv) Calculate by how much the glacier will reduce in thickness between 2010 and 2020, according to the model. [2]

(v) Give one reason why this model will not be suitable in the long term. [1]