The table shows the estimated percentage P of thepopulation of a certain country that are mobile-phone subscribers.(End of year estimates are given.)
| Year | 1997 | 1999 | 2001 | 2003 | 2005 | 2007 |
| P | 2.1 | 8.2 | 15.7 | 25 | 45.7 | 62.5 |
(a) Find the average rate of change of P.
(i) From 2003 to 2007 ........................... percentagepoints per year
(ii) From 2003 to 2005 ............................. percentagepoints per year
(iii) From 2001 to 2003 ............................... percentagepoints per year
(b) Estimate the instantaneous rate of growth in 2003 by taking theaverage of two average rates of change. (Use the average rates ofchange for 2001 to 2003 and 2003 to 2005.)
........................... percentage points per year
(c) Estimate the instantaneous rate of growth in 2003 by sketchinga graph of P and measuring the slope of a tangent. (Sketchyour graph so that it is a smooth curve through the points, and sothat the tangent line has an x-intercept of 1999.3 andpassing through the point
(2006, 46.6).
Round your answer to two decimal places.)
.................................... percentage points per year
