The number N of US cellular phone subscribers (in millions) is shown in the tabl

Question

The number N of US cellular phone subscribers (in millions) is shown in the table. (Midyear estimates are given.)

t 1996 1998 2000 2002 2004 2006

N 44     69   109   141 182   233

(a) Find the average rate of cell phone growth between the following years. In each case, include the units. (Round your answers to one decimal place.) (i) from 1998 to 2004 million phones/yr

(ii) from 2000 to 2002 million phones/yr

(iii) from 1998 to 2000 million phone/yr

(b) Estimate the instantaneous rate of growth in 2000 by taking the average of the two average rates of change in (ii) and (iii). What are its units? million phones/yr

Explanation / Answer

(i) Average rate of celllphone growth from 1998 to 2004 is

N(2004)-N(1998)/2004-1998 = (182-69)/6 = 113/6 = 18.8 million phones/yr

(ii) from 2000 to 2002

(N(2002)-N(2000))/2002-2000 = (141-109)/ 2 = 16 million phones/yr.

(iii) from 1998 to 2000

(N(2000)-N(1998))/2000-1998 = (109-69)/2 =20 million phones/yr.

(b) Instaneous growth rate in yr 2000

is Average of (ii) and (iii) i.e., (20+16)/2 = 18 millions/yr

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