Question 1192979
**a) Find the Explicit Formula**

1. **Calculate the Average Annual Increase:**

   * Find the differences in spending between consecutive years:
      * 2007 - 2005: $56.04 - $38.35 = $17.69
      * 2009 - 2007: $57.27 - $56.04 = $1.23
      * 2011 - 2009: $59.33 - $57.27 = $2.06
      * 2012 - 2011: $63.87 - $59.33 = $4.54

   * Calculate the average annual increase:
      * (17.69 + 1.23 + 2.06 + 4.54) / 4 = $6.38

2. **Write the Explicit Formula:**

   * Since we're assuming linear growth, the formula for the amount spent (Pn) in year n is:
      * Pn = P0 + r * n 
         * where:
            * Pn is the amount spent in year n
            * P0 is the initial amount spent (in 2005) = $38.35
            * r is the average annual increase = $6.38
            * n is the number of years after 2005

   * **Therefore, the explicit formula is:**
      * Pn = $38.35 + $6.38 * n

**b) Predict Spending in 2022**

* Calculate the number of years after 2005:
   * 2022 - 2005 = 17 years

* Use the formula to predict spending in 2022:
   * P17 = $38.35 + $6.38 * 17 
   * P17 = $38.35 + $108.46
   * P17 = $146.81

**The model predicts that $146.81 would be spent on merchandise, apparel, and snacks when watching a Super Bowl game in 2022.**

**Important Note:** This model assumes a constant linear increase in spending each year. In reality, spending patterns may not follow a perfectly linear trend.