A storage locker measures 8 feet wide, 12 feet deep, and 9 feet high. The monthly rental price for the locker is $3.60 per cubic yard. How much does it cost to rent the locker each month? Explain.
PLEASE SHOW WORK!!!

In yards, the dimensions are (8/3), (12/3)=4, and (9/3)=3. The volume of the locker is the product of these dimensions.

Then the rent is

  ($3.60/yd³) × (8/3 yd) × (4 yd) × (3 yd) = $115.20

The rental cost each month is $115.20.

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