Early in the current year, Amazon Co. purchased the Rio Silver Mine at a cost of $30,000,000. The mine was estimated to contain 400,000 tons of ore and to have a residual value of $7,500,000 after mining operations are completed. During the year, 115,000 tons of ore were removed from the mine. At year-end, the book value of the mine is:

a. $23,531,250.
b. $6,468,750.
c. $22,500,000.
d. $30,000,000.

answer

the correct answer is

explanation

the given function is

the excluded values are obtained by solving:

we factor to obtain:

the excluded values are

i believe it's a.

i'm not sure on this one, most likely correct.

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