At the end of a snow storm, Hannah saw there was a lot of snow on her front lawn. The temperature increased and the snow began to melt at a steady rate. Let S
represent the depth of snow on Hannah's lawn, in inches, t hours after the snow
stopped falling. The table below has select values showing the linear
relationship
between t and S. Determine how many hours it would take for the depth of snow to
reach 4.5 inches.

the answer is d. (1.2, -4.7) on edgn

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1. minimum

2. 6400

3. eight

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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