In 2006, there was approximately 233 million cell phone subscribers in the united states. during the next 4 years, the number of cell phone subscribers increased by 6% each year.

a. write an exponential growth model giving the number of cell phone subscribers y (in millions) t years after 2006. estimate the number of cell phone subscribers in 2008.

b. estimate the year when the number of cell phone subscribers was about 278 million.

For this case we have an exponential function of the form:

Where,

Part A:

The equation modeling the problem is given by:

For the year 2008 we have x = 2.

Substituting values:

Part B:

For the year in which the company reaches 278 million we have:

Clearing x we have:

Thus, the company reaches 278 million in the year 2009.

The equation that models the problem is:

For the year 2008 we have:

the company reaches 278 million in the year 2009