Mathematics
MA141 Grantham University Week 4 Pre Calculus Application Paper

MA141 Precalculus

Grantham University

### Question Description

Answer the following questions in a Word document and upload the document to the appropriate drop box. 1) Suppose you deposit \$10,000 into an account earning 3.5% interest compounded quarterly. After n quarters the balance in the account is given by the formula: a) Each quarter can be viewed as a term of a sequence. List the first 5 terms. b) Identify the type of sequence this is. Explain. c) Find the balance in the account after 30 quarters. 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 fall in the first 7 seconds after it is dropped? 3) You borrow \$5,000 from your parents to purchase a used car. The arrangements of the loan are such that you make payments of \$250 per month toward the balance plus 1% interest on the unpaid balance from the previous month. (a) Find the first year’s monthly payments and the unpaid balance after each month. (b) Find the total amount of interest paid over the term of the loan. 4) A tool and die company buys a machine for \$175,000 and it depreciates at a rate of 30% per year. (In other words, at the end of each year the depreciated value is 70% of what it was at the beginning of the year.) Find the depreciated value of the machine after 5 full years. 5) A ball is dropped from a height of 6 feet and begins bouncing. The height of each bounce is three-fourths the height of the previous bounce. Find the total vertical distance the ball travels before coming to rest.

Grantham University

Pre-calculus: MA141

Week Four – Applications Assignment
1. Suppose you deposit \$10,000 into an account earning 3.5% interest compounded
quarterly. After n quarters the balance in the account is given by the formula: a) Each
quarter can be viewed as a term of a sequence. List the first 5 terms. b) Identify the type of
sequence this is. Explain. c) Find the balance in the account after 30 quarters.

a) Each quarter can be viewed as term of a sequence. List the 5 first terms.
0.03 1
10000 ∗ (1 +
) = 10087.50
4
0.03 2
10000 ∗ (1 +
) = 10175.76
4
0.03 3
10000 ∗ (1 +
) = 10264.80
4
10000 ∗ (1 +

0.03 4
) = 10354.62
4

10000 ∗ (1 +

0.03 5
) = 10445.22
4

b) Identify the type of sequence this is. Explain.
The sequence will be arithmetic sequence; the difference is almost the same between the
terms.
c) Find the balance in the account after 30 quarters.
10000 ∗ (1 +

0.03 30
) = 12986.92
4

1

Grantham University

Pre-calculus: MA141

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, 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
fall in the first 7 seconds after it is dropped?

We are finding the 7th term of the sum of an arithmetic series

16 + 48 + 80 + 112 + ⋯
𝑎7 = 𝑎1 + (7 − 1)𝑑
Where:
d: common difference
a7: 7th term
a1: 1st term
𝑎7 = 16 + (7 − 1)(32)
𝒂𝟕 = 𝟐𝟎𝟖 𝒇𝒕
The object fall 208 feet in the first 7 seconds.

2

Grantham University

Pre-calculus: MA141

3. You borrow \$5,000 from your parents to purchase a used car. The arrangements of the
loan are such that you make payments of \$250 per month tow...

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UIUC
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