MATHEMATICS 100 Name:



MATHEMATICS 103 Name: KEY

Section 01

EXAM 03

November 06, 2009

This exam has 3 pages, including this cover page. Please make sure you have all 3 pages.

You have 55 minutes to complete this exam.

You are allowed to work with one partner. If you do work with a partner, just turn in one exam.

This exam is open book and open notebook. You must use your own textbook and notes, no sharing.

You may use your scientific calculator, and you may log-in to the computer at your desk and use a blank Excel spreadsheet or the Windows calculator, but do not print anything out. You are not allowed to use any other application, such as email, a web-browser, instant-messaging, or personal electronic devices such as a cell-phones or MP3 players. There is a "Zero-Tolerance" policy for violation of this policy. That is if you use any of these applications during this exam, it will be considered a violation of the code on Academic Integrity and you will receive 0 points.

You must show all your work for full credit. Check your answers wherever possible.

The answers you handwrite below will be graded. Do not print anything out.

1. Consider a reading that you are analyzing in one of your classes. You determine that it contains 21 “big words,” 8 sentences, and 204 words total.

[4 pts] Calculate the Fog Index, and give a brief explanation of your result.

Fog Index = ( # words / # sentences + 100 * # “big words” / #words )*0.4

Fog Index = ( 204 / 8 + 100 * 21 / 204 )*0.4 = ( 25.5 + 100*0.10294)*0.4 = 35.79 * 0.4 = 14.3

The passage has a fog index of 14.3, which indicates it is on the college sophomore level.

[4 pts] How would the Fog Index change if there were twice as many sentences (up to 16), but the same number of “big words” and total words?

Fog Index = ( # words / # sentences + 100 * # “big words” / #words )*0.4

Fog Index = ( 204 / 16 + 100 * 21 / 204 )*0.4 = ( 25.5 + 100*0.10294)*0.4 = 23.04 * 0.4 = 9.2

So, if the passage contained the same number of words and big words, but was split up into more, smaller sentences, the reading level would drop to 9.2, or high-school freshman level.

2. In class, we decided the salary for the “all-time greatest summer job” would start at $10,000 for the first summer, and grow by 6% each year.

[4 pts] Give the function, S(t), for the salary, S, as a function of t, the number of years since the initial summer. (Note: this formula should be in your course notes, we discussed it in class).

S(t) = initial salary * (1+rate)t = 10,000 * (1+0.06)t = 10,000 * (1.06)t

[4 pts] Using logarithms, solve for the number of summers since the initial summer, it would take to have a salary of $25,000 or over. Show your work.

25,000 = 10,000 * (1.06)t divide by 10,000

2.5 = (1.06)t take log of each side

log(2.5) = log((1.06)t) apply Property 3 of logs

log(2.5) = t*log(1.06) divide by log(1.06)

log(2.5) / log(1.06)= t solve for t

0.3979 / 0.02531 = 15.72 So, in the 16th year after the initial summer, the salary will be over $25,000.

3. Consider the following two savings account options:

(a) Bank 1offers an APR of 2.9% compounded daily (b) Bank 2, APR of 3.0% compounded monthly

[10 pts] Which Bank would you choose to save your money in? Show your work.

APY is a way of comparing “apples to apples”

Bank 1 APY is (1+APR/n)n = (1+0.029/365)365 = 1.000079452365 = 1.02942 ( 2.942%

Bank 2 APY is (1+APR/n)n = (1+0.03/12)12 = 1.002512 = 1.0304 ( 3.04%

Bank 2’s APY is 3.04%, which is higher than Bank 1’s, so go with (b), Bank 2.

4. Create a set of exam scores (for a 100 point exam), for a hypothetical class of five students, for each scenario below:

[6 pts] The mean and median [6 pts] The Inter-Quartile Range (IQR),

of the scores are the same. defined as Q3 – Q1, is 15.

Just 5 scores make the set an automatic 5-number summary

75, 80, 85, 90, 95 70, 75, 85, 90, 95

mean = median = 85 Q1=75 and Q3=90, 90 – 75 = 15

5. Suppose a new college graduate wants to accumulate $20,000 for a deposit on a home in 5 years by making regular end-of-the-month savings deposits. Assume an APR of 3% compounded monthly.

[8 pts] Set up (you do NOT need to solve it) the equation used to determine the monthly deposit to reach the goal. You do NOT need to actually calculate, just set up the equation.

Just like Example 9.8 on page 160 of the textbook.

Accumulated Savings Formula

A = PMT* ( ( 1 + APR / n )nt – 1) / (APR / n )

20,000 = PMT* ( ( 1 + 0.03 / 12 )12*5 – 1) / (0.03 / 12 )

20,000 = PMT* ( ( 1.0025 )60 – 1) / (0.0025 ) = PMT * 64.6467

20,000 = PMT * 64.6467

309.37 = PMT Save $309.37 per month for 5 years to have $25,000 in 5 years

|Residence Hall |Number of |Standard |

| |Students |Quota |

|QM Palace | 14 |14/4.2 = 3.33 |

|Quanster Hall | 20 |20/4.2=4.76 |

|Staterland Hall | 8 |8/4.2=1.90 |

6. A residence hall governing board is to be formed with

representatives from three student residence halls. The total number

of members on the board will be 10, and representation will be based

on student population of each hall. The number of students in each

of the three halls is given at the right.

[2 pts] Calculate the Standard Divisor.

(14+20+8) / 10 = 42 / 10 = 4.2

[6 pts] Fill in the 3rd column of the table at the right with each hall’s

Standard Quota.

[9 pts] Fill in the following table, and be sure to show your work:

| |QM Palace |Quanster Hall |Staterland Hall |

|Seats apportioned |3.33 ( 3 |4.76 ( 4 |1.90 ( 1 |

|from Hamilton’s |3+4+1 = 8 < 10, need to | | |

|Method |Distribute two more seats | | |

| |.76 and .90 are the two | | |

|You may include |largest fractional parts | | |

|Your intermediate | | | |

|calculations in the |3 |5 |2 |

|table | | | |

[9 pts] If you were using Adams’ method to apportion the seats, and tried a modified divisor of 5.5, how many seats would that give each hall?

QMPalace Quanster Hall Staterland Hall

14/5.5 = 2.55 ( 3 20/5.5 = 3.64 ( 4 8/5.5 = 1.45 ( 2

[4 pts] 5.5 is not a correct choice of modified divisor to apportion these seats using Adams’ Method. Would you make your next modified divisor larger or smaller than 5.5? Why?

No, 3+4+2 = 9, not 10. Make the next divisor smaller than 5.5 so the modified quotients are larger.

7. You take out a 15 year mortgage to purchase a home, and you borrow $100,000, where your loan has an APR of 4.9%, compounded monthly, with one point.

[5 pts] Give the value of variables you would use in the equation to determine the monthly payment.

p = 100,000*1.01 = 101,000 APR = 4.9% or 0.049 n = 12 t = 15

[7 pts] The monthly payment for this mortgage is $793.45. Set up the equation, with the numeric values plugged in, that you would use to calculate this monthly payment. You do NOT need to actually calculate the payment, just set up the equation with the appropriate quantities.

Installment Loan Formula

PMT = p*(APR / n) / ( 1 – (1+APR / n )^-n*t )

PMT = 101000*(0.049 / 12) / ( 1 – (1+0.049 / 12 )^-12*15 )

PMT = 101000*0.0040833 / ( 1 – 1. 0040833^-180) = 412.4167 / (1 – 0.48022) = 412.4167 / 0.519776

PMT = $793.45

[6 pts] Find the amount of interest you will pay in the first month of the loan.

101,000*0.049/12 = 101,000*0.00408333 = 412.42

[6 pts] Find the total amount of interest you will pay over the life of the loan.

Total Interest = Total Amt. Paid – Amt. Borrowed

Total Interest = 793.45*12*15 – 100,000 (subtract off the point too, if only count $101,000 as the amount borrowed)

Total Interest = 142,821.00 – 100,000 = $42,821.00

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|Page Number |Possible Points |Score |

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|2 |46 | |

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|3 |54 | |

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|Total |100 | |

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Project 02 is due on Monday, 09.Nov

Honor Pledge

I am familiar with the policy for Academic Integrity as outlined in the Pathfinder:

(intranet.juniata.edu/policies/pathfinder/acadhonesty.html).

I have not discussed the contents of this exam before it has been administered to me, and I will not discuss the contents of this exam before it is administered to someone else.

I understand that failure to comply with this agreement will constitute cheating and subject me to a charge of academic dishonesty.

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Date

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