Math 1030-7 Practise Final Fall 2010
Name:
Instructor’s Name:
Section:
Instructions: Please note that there are two parts. Part I is worth a total of 30 points. Part II is worth
70 points. Show your work on each question.
The formulas below are provided for your convenience
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This is only a practise final made by the instructor. Problems of the real final won’t
necessarily come from here. But the ideas used in the problems are almost the same.
1
Part I: (30 pts) There are five questions and each question is worth 6 points.
1. One pound of fat is roughly 3500 calories. I’ve got a special 100-watt bulb that is powered by fat.
For how long could 1 pound of fat keep this bulb lit? (Remember that 1 Calorie is 4184 joules.)
Answer
2. The number of daily newspapers in the United States was 2226 in 1900 and 1420 in 2010. Find the
absolute change and relative change.
Absolute change
Relative change
3. Simplify the following expression:
(xy 2 )−2 x4
· 7
x−3 y
y
Answer
4. Jack has a scale model of Washington Monument which is 3 inches tall and weighs 10 pounds. The
real monument is 555 feet tall. Suppose both the model and real monument are made of marble,
what’s the weight of the real Washington Monument approximately? (Please include units.)
Answer
5. (a) A brilliant but twisted programmer writes a computer virus that spreads pretty quickly. When
you get infected, it sends an email to all of your friends (from your computer) with the subject
“i luv u.” Your friends, desperate for your love, open the email and get infected. So in
some sense, this virus is not so much exploiting a vulnerability in computers as much as it
is exploiting a vulnerability in the human condition. If the number of infected computers
increases by 45% per day and there are 600 computers infected already, how many computers
will be infected in 7 days?
Answer
(b) Does this situation represent a linear or exponential model? Why?
Part II (70 pts): There are 7 questions and each question is worth 10 points
1. Jack has an ostrich farm. He started this farm 15 years ago with 400 ostriches, and the number of
ostriches grows exponentially at a rate of 15% per year. (Please include units in your answer.)
(a) How much ostriches do Jack have now in the farm?
Answer
(b) What is the exact doubling time of the number of ostriches in the farm?
Answer
2. Suppose your pet dog weighed 2.9 pounds 1 month after birth and weighted 15 pounds on his
1-year-old birthday.
(a) Based on these two data points, find a linear function that describes how weight varies with
age.
Answer
(b) How old will he be when he weigh 48 pounds?
Answer
2
3. In order to buy a BMW M6 Coupe which is worth about $100,000, you decide to make regular
deposit to a saving account who will pay an annual percentage rate of 1.5% compounded monthly.
(a) Find the annual percentage yield on this account.
Answer
(b) You want to buy it in 4 years. How much should you deposit monthly to accomplish the goal?
Answer
4. After 13 years of quarterly payments of $83, I finally paid off my (fixed rate) mortgage.
(a) If the mortgage had an APR of 9%, what was my starting loan principal?
Answer
(b) How much money did I spend paying off my mortgage?
Answer
(c) How much money did I spend just on the interest?
Answer
5. A running track is shaped like a giant doughnut. The distance from a point on the track’s outer
edge to the center of the region enclosed by the track is 1 mile. The track is comprised of 5 lanes,
each 6 feet wide. Jerry runs along the outside of the track, and Gary runs along the inside of the
track. They each run a single lap. How many more feet has Jerry run than Gary?
Answer
6. If the current annual growth rate of the US population is 0.7%, when will the US population be
110% of its current value?
Answer
7. There are 119 patients in a hospital who are taking medications regularly. Among them, 71 are
taking antibiotics, 59 are taking blood pressure medication and 82 are taking pain medication. 8
patients are taking just blood pressure medication. Moreover, 15 patients are taking antibiotics
and blood pressure medication only, 16 patients are taking blood pressure medication and pain
medication only, and 24 are taking antibiotics and pain medication only.
(a) Draw a Venn diagram to illustrate this information. Use th symbols A, B, and P to represent the set of patients taking antibiotics, blood pressure medication, and pain medication,
respectively.
(b) Use your diagram to answer the following:
How many patients are taking all three kinds of medications?
Answer
How many patients in this hospital are not taking any of these three medications?
Answer
How many patients are taking antibiotics only?
Answer
3