Afrozen yogurt shop offers a rewards system for frequent customers. the graph below represents how much a rewards customer pays based on the number of ounces of frozen yogurt purchased. which statement describes the total amount a rewards customer pays for 10 ounces and 12 ounces of yogurt? a rewards customer earns 2 free ounces of yogurt because the total amount paid for 10 ounces and 12 ounces is the same. a rewards customer pays $5 per ounce because the total amount paid is always increasing. a rewards customer pays $20 for 10 or 12 ounces of yogurt because the total amount paid is increasing. a rewards customer earns 5 free ounces of yogurt because the total amount paid for 10 ounces and 12 ounces is the same.

a frozen yogurt shop offers a rewards system for frequent customers. the graph below represents how much a rewards customer pays based on the number of ounces of frozen yogurt purchased.

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt