Consider the procedure used below to evaluate log 464 +log 42 +log ,128. Step 1: log 464 = 16
1
Step 2: log 42
2=
Step 3: log 4128 = 32
1
Step 4: log 464 +log 42 +log 4128 = 16+=+32
Step 5: 48
Which statement about the solution of this problem is true?
A
The first mistake was made in Step 1.
В.
The first mistake was made in Step 2.
C.
The first mistake was made in Step 3.
D.
Each step is correct.

answer:

a=9

step-by-step explanation: lmk if you need a explanation

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