Week 5

Week 1 Assignment

Mary Ketchum

MAT 126: Survey of Mathematical Methods

Laura Cella

06-11-2012

35: A person hired a firm to build a CB radio tower. The firm charges $100 for labor for the first 10 feet. After that, the cost of labor for each succeeding 10 feet is $25 more than the preceding 10 feet. That is, the next 10 feet will cost $125, the next 10 feet will cost $150, etc. How much will it cost to build a 90-foot tower?

Here is how I think about it: I see that there is a new price every 10 feet. Each new price is $25 added to the previous price. The repeated addition tells us this is an arithmetic sequence. First, I will need to identify the following numbers.

n=the number of terms altogether n=9

d= the common difference d=25

a1= the first term a1=100

an= the last term an=a9 (yet to be computed)

Next I need to compute what a9 is. This is the formula to find the nth term of the sequence, or the 9th term in this case.

an=a1 + (n – 1)*d

a9=100 + (9 -1) *25

a9=100 + 8 *(25)

a9=100 + 200

a9= 300

Now that I know what a9 is, I need to know what the sum of the sequence is for a1 to a9

Sn = (1/2) * n (a1 + an)

S9= (1/2) *9 (100 + 300)

S9= (1/2) *9* (400)

S9= 1800

The final answer is: $1,800

37: A person deposited $500 in a savings account that pays 5% annual interest that is compounded yearly. At the end of 10 years, how much money will be in the savings account?

Here is how I think about it: Each year 5% interest is added to the balance. I will use B as my balance.

B + Balance

B + (0.5) b

B (1+0.5)

B (1.03)

Each year the existing balance is multiplied by 1.05. This is repeated by the same numbers it tells us that we have a geometric sequence. First I need to identify the following numbers.

n= the number of terms n=10

r= the common ratio r=1.05

a1= first term a1=525

500(1.05) = 525 for the balance at the end of the first...