# The number N of locations of a popular coffeehouse chain i

The number N of locations of a popular coffeehouse chain is given in the table. (The numbers of locations as of October 1 are given.)Year20042005200620072008N857510,24412,44315,00716,678(a) Find the average rate of growth between each pair of years.2004 to 2006 locations/year2006 to 2007 locations/year2005 to 2006 locations/year(b) Estimate the instantaneous rate of growth in 2006 by taking the average of the last two rates of change in part (a). locations/year(c) Estimate the instantaneous rate of growth in 2006 by measuring the slope of the tangent line through (2005, 10244) and (2007, 15007). locations/year(d) Estimate the instantaneous rate of growth in 2007 by measuring the slope of the tangent line through (2006, 12443) and (2008, 16678). location/year