Alumber yard has five different lengths of 2 by 4 boards. based on cost per linear foot, which is the best deal available on 2 by 4 boards at this lumber yard?

2 × 4 board prices
8 foot board for $2.95
10 foot board for $3.15
12 foot board for $4.10
16 foot board for $5.80
20 foot board for $6.95

a) 8 foot board for $2.97
b) 10 foot board for $3.25
c) 12 foot board for $4.10
d) 16 foot board for $5.80

The Answer is B.

2.97/8= .371

3.25/10= .325

4.10/12= .342

5.80/16= .366

This means you can get 1 board for $0.325 when buying 10 boards.

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