The following data represent the number of basic cable TV subscribers in the United States.A market researcher believes that external factors, such as satellite TV, have affected the growth of cable subscribers. She is interested in building a model that can be used to describe the number of cable TV subscribers in the United States.

Year ………………………………… Subscribers (1,000)

1975 (t = 5) ……………………………………… 9,800

1980 (t = 10) …………………………………… 17,500

1985 (t = 15) …………………………………… 35,440

1990 (t = 20) …………………………………… 50,520

1992 (t = 22) …………………………………… 54,300

1994 (t = 24) …………………………………… 58,373

1996 (t = 26) …………………………………… 62,300

1998 (t = 28) …………………………………… 64,650

2000 (t = 30) …………………………………… 66,250

2002 (t = 32) …………………………………… 66,472

2004 (t = 34) …………………………………… 65,727

2006 (t = 36) …………………………………… 65,319

(a) Using a graphing utility, draw a scatter diagram of the data using the number of years after 1970, t, as the independent variable and number of subscribers as the dependent variable.

(b) Using a graphing utility, build a logistic model from the data.

(c) Using a graphing utility, draw the function found in part (b) on the scatter diagram.
(d) Based on the model found in part (b), what is the maximum number of cable TV subscribers in the United States?
(e) Use the model found in part (b) to predict the number of cable TV subscribers in the United States in 2015.