The following table shows retail sales in drug stores in billions of dollars in the U.S. for years since 1995. Year Retail Sales 0 85.851 3 108.426 6 141.781 9 169.256 12 202.297 15 222.266 Let S(t)S(t) be the retails sales in billions of dollars in t years since 1995. A linear model for the data is F(t)=9.44t+84.182F(t)=9.44t+84.182. 36912158090100110120130140150160170180190200210220 Use the above scatter plot to decide whether the linear model fits the data well. The function is a good model for the data. The function is not a good model for the data Estimate the retails sales in the U. S. in 2011.  billions of dollars. Use the model to predict the year in which retails sales will be $245 billion.

The table lists the cost in millions of dollars for a 30-second commercial for selected years. Year 1994 1998 2004 2008 2011 Cost 33.7 34.2 35.0 35.5 35.9 a. Find a linear function f that models the data. b. Estimate the cost in 2010 and compare the estimate to the actual value of $36.6 million. Did your estimate involve interpolation or extrapolation? a. Use linear regression to determine the equation of the line that best fits the data. The linear function is f(x) = (Type an expression using x as the variable. Use integers or decimals for any numbers in the expression. Round to three decimal places as needed.)

The below data represent the advertising expenditure and sales of Liu Liu Ltd from year 2010 to 2019. Table: Advertising Expenditure vs. Sales from 2010 to 2019   Year Advert. Expenditure   Sales Growth rate of Ad. Expenditure Growth rate of Sales   (x, £000) (y, £000)     2010 19 84     2011 22 108 18% 29% 2012 32 82 46% -24% 2013 42 86 32% 6% 2014 47 84 11% -3% 2015 46 94 -2% 11% 2016 58 103 27% 10% 2017 63 115 8% 12% 2018 70 106 11% -8% 2019 80 142 15% 34% Total 479 1004       a. What is the statistical relationship shown in the table and list out 3 characteristics of this relationship?

The idea of a large, stable middle class (defined as those with annual household incomes in 2010 between $42,000 and $126,000 for a family of three), is central to America's sense of itself. But the U.S. middle class shrank steadily from 61% of all adults in 1971  (t = 0)  to 51% in 2011  (t = 4),  where t is measured in decades. Research has shown that this decline was approximately linear.† (a) Find a linear function f(t) giving the percentage of middle-income adults in decade t, where t = 0 corresponds to 1971. (b) If this trend continues, what will the percentage of middle-income adults be in 2041?