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.)

(a) Find the average rate of cell phone growth between the following years. (Round your answers to one decimal place.)

(i) from 1998 to 2004 (million phones/yr)

(ii) from 2002 to 2004 (million phones/yr)

(b) Estimate the instantaneous rate of growth in 2002 by taking the average of the two average rates of change in (ii) and (iii). (million phones/yr)

Explanation / Answer

(a) (i) From 1998 to 2004

Average rate of cell phone growth = [ N(2004) - N(1998) ]/(2004 - 1998)

==> [ 182 - 69]/(6)

==> 113/6

==> 18.33

Hence average rate of cell growth from 1998 to 2004 is 18.33 million phones/year

(ii) From 2002 to 2004

Average rate of cell phone growth = [ N(2004) - N(2002) ]/(2004 - 2002)

==> [ 182 - 141]/(2)

==> 41/2

==> 20.5

Hence average rate of cell growth from 2002 to 2004 is 20.5 million phones/year

(b) Instantaneous rate of growth in 2002 = (18.33 + 20.5 )/2

==> 38.83/2

==> 19.42

Hence Instantaneous rate of growth in 2002 = 19.42 million phones / year

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