Suppose the rate of change of the percent P of U.S. households with cable/satellite TV can be

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Suppose the rate of change of the percent P of U.S. households with cable/satellite TV can be modeled by
dP 46.3 dt t+5

where t is the number of years past 1975.
(a) Use integration and the data point for 2010 to find the function P(t) that models the percent of U.S. households with cable/satellite TV.
(b) How well does the model from part (a) fit the data in the table?
(c) If the model remains valid, use it to predict the percent of U.S. households with cable/satellite TV in 2018.

Year Year Percent Percent 22.6 46.2 1980 1985 1990 1995 2000 2005 2010 2013 67.8 85.7 90.6 90.5 59.0 65.7
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