1a. Consider the sequence {?? }n≥0 which starts 1,2,7,20,61,122,..., defined by the recurrence relation ?? = 2??−1 + 3??−2 and initial conditions ?0 = 1, ?1 = 2. Solve the recurrence relation. That is, find a closed formula for ??. Show your work.

The abandoned field behind your house is home to a large prairie dog colony. Each week the size of the colony triples. However, sadly 4 prairie dogs die each week as well (after the tripling occurs). Consider the sequence ?0, ?1, ,a2,..., where ?? is the number of prairie dogs in the colony after n weeks.

(b) Write down a recurrence relation to describe an and briefly explain.

(c) Explain why if ?? is even, then ??+1 must also be even.

(d) Suppose you wanted to prove by mathematical induction that an was always even. What would the base case be and why is it needed? Your answer should be specific to this context.

(e) Your friend believes what you have written in parts (b) and (c), but still does not see why ?3 must be even because he does not understand the logic behind induction. Explain why induction in this case proves that there will be an even number of prairie dogs in week 3 specifically

Please with clear legible hand writing, and number your work.

QUESTION 11

1. Garner-Wagner Manufacturing Inc. is considering some new equipment whose data are shown below. The equipment has a 3-year tax life and would be fully depreciated by the straight-line method over 3 years, but it would have a positive pre-tax salvage value at the end of Year 3, when the project would be closed down. Also, some new working capital would be required, but it would be recovered at the end of the project's life. Revenues and other operating costs are expected to be constant over the project's 3-year life.

   Project cost of capital (r)                                                                  10.0%

   Net investment in fixed assets (depreciable basis) $200,000

   Required new working capital                                                          $30,000

   Straight-line depreciation rate                                                        33.3333%

   Sales revenues, each year $150,000

   Operating costs (excl. depreciation), each year $75,000

   Expected pretax salvage value $15,000

   Tax rate                                                                                             35.0%

   What is the project’s operating cash flows from Year 1 to Year 3 for Garner-Wagner Manufacturing Inc.?

   		$62,234.33
   		$65,478.67
   		$68,742.33
   		$72,083.33
   		$74,093.67

10 points   

QUESTION 12

1. Using information from Question 11. What is the project's NPV for Garner-Wagner Manufacturing Inc.?

   		$10,245.23
   		$(20,874.66)
   		$21,005.45
   		$(12,155.78)
   		$(15,363.17)

Assume the following people are interviewed by a representative of the Bureau of Labor Statistics. Classify each as either employed, unemployed, or not in the labor force. For each scenario, explain why you classified the person the way you did.

1. Nancy Lopez reported to the interviewer that last week she worked 30 hours as a sales manager for the Coca-Cola Bottling company.
2. Bill Stevens lost his job when the local plant of Arco Steel Company was closed down. Since then, he has been visiting the personnel offices of the other factories in the town trying to find a job.
3. Patricia Hunter is a homemaker. Last week, she was occupied with her normal household chores. She neither held a job nor looked for a job. Her 75-year old father, Jake Jackson, lives with her and has not worked nor looked for work because of a disability.
4. Julie Simon is an autoworker. Last week she was not working because her union is on strike against the local automaker.
5. Tom Nguyen is a personnel director. Last week he was not working because he had problems finding child care for his two small children.
6. Explain how the natural rate of unemployment is determined.
7. Should the main macroeconomic aim of the government be full employment? Please explain your response.

Option #1: Acquisition Costs: Land and Building

You are the project manager at Janson Manufacturing. Feedback from the annual employee’s survey revealed that employees were interested in having a fitness center. Thus, last week, you closed the deal and purchased land and a building for $6 million. Other expenses incurred in connection to this purchase included:

An independent appraisal was requested to determine the individual fair value estimates. The land appraised at $5.5 million and the building at $1.9 million.

Spending on the property started right away. Janson installed fences and completed the driveway at a cost of $45,000 and $75,000, respectively.

Required:

1. What is the initial valuation of each asset Janson purchased in these transactions?
2. Suppose Janson, immediately after acquiring the property, decided to tear down the building. The cost of the removal of the building was $350,000 and salvaged materials sold for $8,000. An additional $100,000 was paid to grade the land for building the new fitness center. What is the initial valuation of each asset Janson acquired in this transaction?

Answers must be submitted in an Excel file showing all calculations used to arrive at the final answers. Provide comments on the spreadsheet to explain the rationale for the amounts recorded.

1. Explain the difference between a closed-ended question, an open-ended question, and
a probing question. When would you use each?
2. Explain the difference between a top-down and bottom- up interview approach. When
would you use each approach?
3. Draw a use case diagram for the following dentist office system, but do not bother to
identify the flow of events within each use case. Whenever new patients are seen for
the first time, they complete a patient information form that asks their name,
address, phone number and brief medical history, which are stored in the patient
information file. When a patient calls to schedule a new appointment or change an
existing appointment, the receptionist checks the appointment file for an available
time. Once a good time is found for the patient, the appointment is scheduled. If the
patient is a new patient, an incomplete entry is made in the patient file; the full
information will be collected when they arrive for their appointment. Because
appointments are often made so far in advance, the receptionist usually mails a
reminder postcard to each patient two weeks before their appointment.
4. Create an activity diagram for the dentist office system in previous question.
5. Create one detail use-case description for the dentist office system in previous
question.

draw and label one or two separate ad-as models to show recessionary and inflation gaps (5%). Then discuss how neoclassicals recommend each of recessionary and inflationary gaps to be closed to return to an economy with full employment (10%).

Explain why have some developing countries such as South Korea managed to close the development gap and catch up economically with the developed countries?

How South Korea closed the development gap and reach the developed countries?

The pH of a water is measured to be 7.0. The concentration of bicarbonate was measured to be 1.3*10^-3 M. What are the concentrations of carbonate, carbonic acid, and CT (total carbonates)? Assume this system is closed to the atmosphere and the temperature is 25 C.

At a certain temperature, the Kp for the decomposition of H2S is 0.842.

Initially, only H2S is present at a pressure of 0.126 atm in a closed container. What is the total pressure in the container at equilibrium?

H2S (g) <---> H2(g) + S(g)

What does economic theory suggest is the long run relationship between changes in a country’s level of savings and its level of investment? Explain how your answer depends upon whether or not the economy is open or closed.