math

Exam 1

Instructions:You are allowed to work with one other person from the class on this exam. However, both individuals are responsible for writing up their own work for each problem. If you didn’t work with a partner, then indicate so below. Please write all solutions on separate paper, and attach this cover sheet to your exam. You are allowed to use any inanimate sources you wish to complete the exam. You must show all work to receive full credit. If you have any questions about the exam feel free to email me or ask me in person.

Test Integrity Statement: I, (your name:) , certify that I did not discuss this exam with any individual other than (your partner’s name:)

. I also certify that I was responsible for writing up my own solutions on this exam.

Signature:

Partner’s Signature:

Concept Questions:

1) In the following table, is D a function of E? is E a function of D? Why? (20 points)

D E 3.47 1 2.12 0 -1.09 -1 2.12 0 -1.89 -1 3.47 1 -1.09 -1

2) In the following table, is Q a linear function of t? Why or why not? (10 points)

t Q .13 37 .26 41 .52 45 1.04 49

3) What is the domain of the function f? What is the range of the function g? Explain your work (10 points).

f(x) =

p �x2 + 3

5x2 + 5x � 10 g(x) =

1

3x � 2 1

2

4) A school wants to build a fenced in rectangular playground. One pair of opposite sides of the playground will cost $20/ft. The other pair of sides will cost $13 dollars per foot. If the school has a budget of $1200 for the fencing, what are the dimensions of the largest area the school can enclose for the playground? Explain your process. How do you know you have found the maximum? Hint: find equations for the cost and area and see what you can do with them. (10 points).

Modeling Questions: Please select two of the following three problems to write a small science paper on. Your write up should include explanations for all calculations, an in- troduction where you describe your approach to the problem and layout all assumptions and sources for all relevant values, and a conclusion where you discuss possible sources of error or inaccuracies of your model. You write-ups will be graded based on the attached rubric. You do not need to make a bibliography, but you should identify any sources you use.

1) Create a mathematical model for a zombie apocalypse. In analyzing your model you may want to consider the following questions: What does your model predict for the outcome of the zombie apocalypse? What is the practical domain and range of the model? What do the parameters of your model tell you?

2) When will your college education have paid for itself? Make sure to employ the use of functions were appropriate when answering this question. You may also want to consider opportunity costs in addition to the tuition you pay.

3) Empirically verify the formula for the height of a falling object:

h(t) = �4.9t2 + v0t + h0. One way to do this would be to drop an object from a building or bridge and time how long it takes to hit the ground. Compare the measured times with the time predicted by the above model. You may want to preform multiple trials. (remember the above formula is only valid for units of meters and seconds).