Mr. Snow keeps a list of vocabulary terms that he wants his students to memorize from the textbook. He began the year with 15 terms on the list. Of the 35 new terms in each chapter, Mr. Snow puts the definitions of 10 terms on the wall and adds the remaining terms to the vocabulary list to be memorized.

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This question has 3 parts. Be sure to complete all parts.
A
Type your response in the box.
The number of terms on the vocabulary list can be represented by a linear function. Identify the rate of change and intial value of this function. Explain what these values represent in terms of the situation.

the answer would be 484

step-by-step explanation:

just multiply 0.484 times 1,000 (formula)

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