The number of cell phone subscribers in the United States between the years 2000 and 2010 is approximated by the function

Question

The number of cell phone subscribers in the United States between the years 2000 and 2010 is approximated by the function

N(t) = 385.474

1 + 2.521e−0.214t

    (0 ≤ t ≤ 10)

How many cell phone subscribers were there in the United States in 2000? (Round your answer to one decimal place.) million subscribers. If the trend continued, how many subscribers were there in 2012? (Round your answer to one decimal place.) million subscribers

Answer 1

1) How many cell phone subscribers were there in the United States in 2000?

N(t) is the number of subscribers in millions as a function of time which we are given to be 385.474

We are also given the function N(t) / 1 + 2.521e^−0.214t where N(t) = 385.474

^{t is our time which is an equality}  (0 ≤ t ≤ 10)

Set t=0 (This would be equivalent to the year 2000)

385.474 / 1+2.521e^−0.214(0)

385.474 / 1+2.521e^{0 ---->} (e⁰ = 1)

385.474 / 3.521 = 109.4786

In the year 2000, or t=0, there are 109.5 million subscribers in the U.S.

2) If the trend continued, how many subscribers were there in 2012?

In 2012, t = 12

Our formula stays the same as stated in the problem

Set t=12

385.474 / 1+2.521e^−0.214(12)

385.474 / 1+2.521*(0.07668876968) (carry more decimals and only round at the end for the correct answer. If you are using the calculator use the exact number)

385.474/ 1.19333238838 = 323.023160817

In the year 2012, if the same trend occurs, 323.0 million subscribers in the U.S.