the number n of us cellular phone subscribers (in millions) is shown in the table. (midyear estimates are…

the number n of us cellular phone subscribers (in millions) is shown in the table. (midyear estimates are given.)\n\n(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.)\n(i) from 2002 to 2006\n\nmillion phones/yr\n\n(ii) from 2000 to 2002\n\nmillion phones/yr\n\n(iii) from 1998 to 2000\n\nmillion phone/yr\n\n(b) estimate the instantaneous rate of growth in 2000 by taking the average of the two average rates of change in (ii) and (iii).\n\nmillion phones/yr\n\nresources\nread it

the number n of us cellular phone subscribers (in millions) is shown in the table. (midyear estimates are given.)\n\n(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.)\n(i) from 2002 to 2006\n\nmillion phones/yr\n\n(ii) from 2000 to 2002\n\nmillion phones/yr\n\n(iii) from 1998 to 2000\n\nmillion phone/yr\n\n(b) estimate the instantaneous rate of growth in 2000 by taking the average of the two average rates of change in (ii) and (iii).\n\nmillion phones/yr\n\nresources\nread it

Answer

Explanation:

Step1: Recall the formula for average rate of change

The average rate of change of a function (y = f(x)) over the interval ([x_1,x_2]) is given by (\frac{f(x_2)-f(x_1)}{x_2 - x_1}). Here, (N) is a function of (t) (where (t) represents the year), and the average rate of change is (\frac{N(t_2)-N(t_1)}{t_2 - t_1})

Step2: Calculate the average rate of change from 2002 to 2006

For (t_1 = 2002), (N(t_1)=141); for (t_2 = 2006), (N(t_2)=233). [ \begin{align*} \frac{N(2006)-N(2002)}{2006 - 2002}&=\frac{233 - 141}{4}\ &=\frac{92}{4}\ & = 23.0 \end{align*} ]

Step3: Calculate the average rate of change from 2000 to 2002

For (t_1 = 2000), (N(t_1)=109); for (t_2 = 2002), (N(t_2)=141). [ \begin{align*} \frac{N(2002)-N(2000)}{2002 - 2000}&=\frac{141-109}{2}\ &=\frac{32}{2}\ &=16.0 \end{align*} ]

Step4: Calculate the average rate of change from 1998 to 2000

For (t_1 = 1998), (N(t_1)=69); for (t_2 = 2000), (N(t_2)=109). [ \begin{align*} \frac{N(2000)-N(1998)}{2000 - 1998}&=\frac{109 - 69}{2}\ &=\frac{40}{2}\ &=20.0 \end{align*} ]

Step5: Calculate the instantaneous rate of growth in 2000

We take the average of the average - rate of change from 1998 to 2000 and from 2000 to 2002. [ \begin{align*} \frac{16.0+20.0}{2}&=\frac{36}{2}\ & = 18.0 \end{align*} ]

Answer:

(i) (23.0) million phones/yr (ii) (16.0) million phones/yr (iii) (20.0) million phones/yr (b) (18.0) million phones/yr