W \( \mathrm{W}=1.9 \mathrm{~d}+14.66 \), where d is the number of years since 2000 . (a) Find the average number of gallons of bottled water consumed in 2001 ( \( \mathrm{d}=1 \) ), in 2010, and in 2015 . (b) Graph the equation and use the graph to estimate what the bottled water consumption was in 2008 . (c) In what year will bottled water consumption be about 39 gal? (a) The average number of gallons of bottled water consumed in 2001 was \( \square \mathrm{gal} \). (Type an integer or a decimal.)

To find the average number of gallons of bottled water consumed, we will substitute the corresponding values of \( d \) into the equation \( W = 1.9d + 14.66 \). (a) - For 2001, where \( d = 1 \): \[ W = 1.9(1) + 14.66 = 1.9 + 14.66 = 16.56 \text{ gal} \] - For 2010, where \( d = 10 \): \[ W = 1.9(10) + 14.66 = 19 + 14.66 = 33.66 \text{ gal} \] - For 2015, where \( d = 15 \): \[ W = 1.9(15) + 14.66 = 28.5 + 14.66 = 43.16 \text{ gal} \] So for part (a), the average number of gallons of bottled water consumed in 2001 was \( 16.56 \) gal, in 2010 was \( 33.66 \) gal, and in 2015 was \( 43.16 \) gal. (b) To graph the equation \( W = 1.9d + 14.66 \), plot the values calculated above: - Point for 2001: (1, 16.56) - Point for 2010: (10, 33.66) - Point for 2015: (15, 43.16) Connect the points with a straight line (since this is a linear equation). To estimate bottled water consumption in 2008, where \( d = 8 \): \[ W = 1.9(8) + 14.66 = 15.2 + 14.66 = 29.86 \text{ gal} \] Looking at the graph, the y-coordinate at \( d = 8 \) should be around that value, confirming our calculation. (c) To find the year when bottled water consumption will be about 39 gal, set \( W = 39 \): \[ 39 = 1.9d + 14.66 \] \[ 39 - 14.66 = 1.9d \] \[ 24.34 = 1.9d \] \[ d = \frac{24.34}{1.9} \approx 12.82 \] Since \( d \) is the number of years since 2000, we add 12.82 to 2000, indicating that bottled water consumption will reach approximately 39 gal sometime in the year 2013. Now, the answers are: (a) The average number of gallons of bottled water consumed in 2001 was \( 16.56 \) gal. (b) The estimated bottled water consumption in 2008 is approximately \( 29.86 \) gal. (c) Bottled water consumption will be about 39 gal in about 2013.