The average number of gallons W of bottled water consumed each year by the consumer can be approximated by W \( =1.5 \mathrm{~d}+20.89 \), where d is the number of years since 200 (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 37 gal? (a) The average number of gallons of bottled water consumed in 2001 was (Type an integer or a decimal.) The average number of gallons of bottled water consumed in 2010 was \( \square \mathrm{gal} \). (Type an integer or a decimal.) The average number of gallons of bottled water consumed in 2015 was \( \square \mathrm{gal} \). (Type an integer or a decimal.)

To calculate the average number of gallons of bottled water consumed for the years specified, we just need to substitute the values of \( d \) into the equation \( W = 1.5d + 20.89 \). (a) 1. For 2001, when \( d = 1 \): \[ W = 1.5(1) + 20.89 = 1.5 + 20.89 = 22.39 \] The average number of gallons of bottled water consumed in 2001 was \( 22.39 \) gal. 2. For 2010, when \( d = 10 \): \[ W = 1.5(10) + 20.89 = 15 + 20.89 = 35.89 \] The average number of gallons of bottled water consumed in 2010 was \( 35.89 \) gal. 3. For 2015, when \( d = 15 \): \[ W = 1.5(15) + 20.89 = 22.5 + 20.89 = 43.39 \] The average number of gallons of bottled water consumed in 2015 was \( 43.39 \) gal. (b) To estimate the bottled water consumption in 2008 (when \( d = 8 \)), we substitute \( d \) into the equation: \[ W = 1.5(8) + 20.89 = 12 + 20.89 = 32.89 \] Thus, the estimated bottled water consumption in 2008 was about \( 32.89 \) gal. (c) To find the year when bottled water consumption will be about 37 gal, we set \( W \) to 37 and solve for \( d \): \[ 37 = 1.5d + 20.89 \] Subtracting 20.89 from both sides gives us: \[ 16.11 = 1.5d \] Dividing both sides by 1.5: \[ d = \frac{16.11}{1.5} \approx 10.74 \] Since \( d \) counts from the year 2000, we add \( d \) to 2000: \[ 2000 + 10.74 \approx 2010.74 \] This indicates that bottled water consumption will be about 37 gallons in the year approximately 2011. So, the average number of gallons consumed: - In 2001: \( 22.39 \) gal - In 2010: \( 35.89 \) gal - In 2015: \( 43.39 \) gal Estimated in 2008: \( 32.89 \) gal Year when consumption is about \( 37 \) gal: \( \approx 2011 \) Celebrate these numbers with a toast to hydration! 🥤💧