Chapter 6.1, Problem 23E

a

To determine

Write an exponential growth model giving the number of cell phone subscriber and also estimate the number of phone subscriber in 2008.

Answer to Problem 23E

Thenumber of phone subscriber in 2008 is $261.80$

Explanation of Solution

Given information :

In 2006,there were approximate 233 millions cell phone subscribers in the United States. During the next 4 years, the number of cell phone subscriber increase by about 6%.

The exponential growth model is $y=a{\left(1+r\right)}^t$

The exponential growth model giving the number of cell phone subscribers $y$ (in millions) $t$ in times is $y=233{\left(1+0.06\right)}^t$

Therefore ,the number of cell phone subscriber in 2008 is

  $\begin{array}{l}y=233{\left(1+0.06\right)}^t\\ y=233{\left(1.06\right)}^2\\ y=261.80\end{array}$

Hence, the number of phone subscriber in 2008 is $261.80$

b

To determine

To estimate the year when the number of cell phone subscriber was about 278 million.

Answer to Problem 23E

The time when the number of cell phone subscriber was about 278 million is 3.03 years

Explanation of Solution

Given information :

In 2006,there were approximate 233 millions cell phone subscribers in the United States. During the next 4 years, the number of cell phone subscriber increase by about 6%.

Use the trace feature of a graphing calculator to determine that $y=278$ when $t=3.03$ . After 3.03 year thecell phone subscriber was about 278 million.

  

Hence, thetime when the number of cell phone subscriber was about 278 million is 3.03 years.