A new exhibit is scheduled to open at a local museum. Museum officials expect that 9000 people will visit the exhibit in its first week, and the number of visitors will drop by 10 people per week after the first week. Write a general
term formula to describe the number of visitors expected each week. Then find the number of visitors expected in
the exhibit's 11 week. what is the general term formula?

1

step-by-step explanation:

it's the only multiple of both and the least

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

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the answer to this would be 5x^3-6x^2-24 over 3x^2

hope this if needed hmu