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

Answer 1

The average rate of cell phone growth from 1998 to 2004 is 18.8 million phones/year, from 2000 to 2002 is 16 million phones/year, and from 1998 to 2000 is 20 million phones/year. The estimated instantaneous rate of growth in 2000 is 18 million phones/year.

Step-by-step explanation:

(a) To find the average rate of cell phone growth, we need to calculate the change in the number of subscribers divided by the number of years. (i) From 1998 to 2004, the change in the number of subscribers is 182 million - 69 million = 113 million. The number of years is 2004 - 1998 = 6 years. The average rate of growth is 113 million / 6 years = 18.8 million phones/year. (ii) From 2000 to 2002, the change in the number of subscribers is 141 million - 109 million = 32 million. The number of years is 2002 - 2000 = 2 years. The average rate of growth is 32 million / 2 years = 16 million phones/year. (iii) From 1998 to 2000, the change in the number of subscribers is 109 million - 69 million = 40 million. The number of years is 2000 - 1998 = 2 years. The average rate of growth is 40 million / 2 years = 20 million phones/year.

(b) To estimate the instantaneous rate of growth in 2000, we can take the average of the two average rates of change calculated in parts (ii) and (iii). The average rate of growth in 2000 is (16 million phones/year + 20 million phones/year) / 2 = 18 million phones/year.