100 points! a water tank is being drained. the table shows the number of gallons, g, of water left in the tank after h hours. the drainage rate will remain the same. table: h(hours); 1,2,3,4. g(gallons) ; 384,288,216,162. part a: what type of sequence can be used to model the number of gallons remaining? explain your answer. part b: write the recursive formula to express gh, the number of gallons left in the tank after h hours, in terms of the number of gallons left in the tank the previous hour, gh-1. part c: write the explicit formula to express gh, the number of gallons left in the tank after h hours. part d: use your explicit formula from part c to find the number of gallons of water left after 12 hours. show all your work, round your answer to the nearest gallon. part e: convert your final answer from part d into quarts, show all work. k

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

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step-by-step explanation:

seems like d

step-by-step explanation: