An economist predicts that the cost of food will increase by 4% per year for the next several years. a. use the economist’s prediction to write an explicit rule for a geometric sequence that gives the cost in dollars of a box of cereal in year n that costs $3.20 in year 1.

If the cost is expected to rise by 4% per year, then that is equivalent to taking the previous year's price and multiplying it by 104%, or 1.04.
   So a box of cereal costing $3.20 in year 1 will in year 2 cost $3.20*1.04, in year 3 $3.20*1.04*1.04, and so on. If n is the year, then we are simply multiplying the year 1 cost by n-1 to yield the year n cost.
   Expressing this as a geometric sequence, we can say that C(n) = $3.20*1.04^(n-1) for the cost C in year n.