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precal
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Explanation & Answer
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1) Suppose you deposit $10,000 into an account earning 3.5% interest
compounded quarterly. After n quarters the balance in the account, we have this
formula:
10000 (1 +
0.03 𝑛
)
4
a) Each quarter can be viewed as a term of a sequence. List the first 5 terms.
Probably 𝑛 should start from 1:
0.03 1
0.03
10000 (1 +
) = 10000 ∙ (1 +
) = 𝟏𝟎𝟎𝟕𝟓,
4
4
0.03 2
0.03 1
0.03
10000 (1 +
) = 10000 (1 +
) ∙ (1 +
) ≈ 𝟏𝟎𝟏𝟓𝟎. 𝟓𝟔,
4
4
4
10000 (1 +
0.03 3
0.03 2
0.03
) = 10000 (1 +
) ∙ (1 +
) ≈ 𝟏𝟎𝟐𝟐𝟔. 𝟔𝟗,
4
4
4
0.03 4
0.03 3
0.03
10000 (1 +
) = 10000 (1 +
) ∙ (1 +
) ≈ 𝟏𝟎𝟑𝟎𝟑. 𝟑𝟗,
4
4
4
0.03 5
0.03 4
0.03
10000 (1 +
) = 10000 (1 +
) ∙ (1 +
) ≈ 𝟏𝟎𝟑𝟖𝟎. 𝟔𝟕.
4
4
4
b) Identify the type of sequence this is. Explain.
It is a geometric sequence because each next term may be obtained from the previous by
multiplying by the same number 1 +
0.03
4
.
c) Find the balance in the account after 30 quarters.
It is the 30th term and it is equal to 10000 (1 +
0.03 30
4
)
≈ $𝟏𝟐𝟓𝟏𝟐. 𝟕𝟐.
2) An object with negligible air resistance is dropped from the top of the Willis Tower in Chicago
at a height of 1451 feet. During the first second of fall, the object falls 16 feet; during the
second second, it falls 48 feet; during the third second, it falls 80 feet; during the fourth
second, it falls 112 feet. Assuming this pattern continues, how many feet does the object
...