This table represents the monthly fees for checking accounts at two banks. Which statement is best supported by the information in the table?

The fee at Sunrise Bank will be less than the fee at Riverside Bank only when the checking account balance is more than $400.

The fee at Sunrise Bank will be more than the fee at Riverside Bank only when the checking account balance is less than $400.

The fee at Sunrise Bank will always be less than the fee at Riverside Bank.

The fee at Sunrise Bank will be the same as the fee at Riverside Bank only when the checking account balance is $400.
Bank Monthly fee
Sunrise 1% of checking account balance
Riverside $4

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

(−$11) ⋅ 12

deductions are negative and there are 12 months in a year