1 Name _____________________________ MTH129 Fall .docx
- 1. 1 Name: _____________________________ MTH129 Fall 2018 - FINAL EXAM A Show all work neatly on paper provided. Label all work. Place final answers on the answer sheet. PART I: Omit 1 complete question. Place an “X” on the problems & answer space you are omitting. 1. Find the inverse of the following functions: a. �(�) = 2� − 3 b. �(�) = 3� +1 �−2 2. If �(�) = � 2 − 2� + 3 and �(�) = −3� + 4, find the following: a. (�°�)(�) b. (�°�)(2)
- 2. 3. Find the domain for the following expression: a) √� + 5 �) 7� 2 + 3� − 1 �) � 2+4 � 2−9 4. Find the radian measures of the angles with the given degree measures. a) 81° Find the degree measures of the angles with the given radian measures. b) 13� 6 5. Solve the following equations: a) (5t) = 20 b) 6000 = 40(15)t 6. Expand the following logarithmic expressions: a. log(��2 )
- 3. b. ln( 4 √3 ) 7. Describe how the graph of each function can be obtained from the graph f a. � = �(�) − 8 b. � = �(� + 4) − 5 8. A real number t is given � = 2� 3 a. Find the reference number for t. b. Find the terminal point P(x,y) on the unit circle determined by t c. The unit circle is centered at __________________ and has a radius of _________________ PART II: Omit 1 complete question. Place an “X” on the problems & answer space you are omitting.
- 4. 2 1. A sum of $7,000 is invested at an interest rate of 4 1 2 % per year, compounding monthly. (round all answers to the nearest cent) a. Find the amount of the investment after 2 1 2 years. b. How long will it take for the investment to amount to $12,000? c. Using the information in part (a), find the amount of the investment if compounded quarterly. 2. When a company charges price p dollars for one of its products, its revenue is given by � = �(�) = 500�(30 − �) a. Create a quadratic function for price with respect to revenue. b. What price should they charge in order to maximize their revenue? c. What is the maximum revenue? d. What would be the revenue if the price was set at $10?
- 5. e. Sketch a rough graph – indicate the intercepts and the maximum coordinates. 3. The charges for a taxi ride are an initial charge of $2.50 and $0.85 for each mile driven. a. Write a function for the charge of a taxi ride as a linear function of the distance traveled. b. What is the cost of a 12 mile trip? c. Find the equation of a line that passes through the following points: (1,-2) , (2,5) Express in � = �� + � form d. Graph part ( c ) 4. a. Divide the following polynomial and factor completely. �(�) = 3� 4 − 9� 3 − 2� 2 + 5� + 3; � = 3 b. Given polynomial−� 2 + 5� − 6, state the end behavior of its graph. c. Using the polynomial on part ( c ), would this graph have a maximum or a minimum? State why. 5. An item cost $1.00 in 2000. The same item $1.37 in the year 2014. Let’s assume that the growth of the dollar is following an exponential pattern. (Round rates to the 6th decimal place; money to the nearest cent) a. Find an exponential function that will model the data given above.
- 6. b. How much would the item cost in 2010? c. When would the item cost $1.50? 6. Given rational function � = �2−�−2 �2−2�−3 , determine the following: a. x intercept (s) b. y – intercept(s) c. vertical asymptote(s) d. horizontal asymptote(s) 7. a. Determine if the following point lies on the unit circle and state why it does or why it does not: ( 4 5 , − 3 5 ) b. For the given value � = − 3� 4
- 7. : Find the values of sin t , cos t and tan t c. For part ( b) state what quadrant the point land in. 8. a. A 20 foot ladder leans against a building so that the angle between the ground and the ladder is 72°. How high does the ladder reach on the building? (draw a sketch to help you) b. 5. Use the Law of Cosine and the Law of Sine to find the remailing parts of the triangle: � = 130°; � = 5; � = 7 3 FORMULAS: �2 + �2 = � 2 � = − � 2� � = −�±√�2−4�� 2�
- 8. � = �(1 + � � )(�∗ �) � = �0 + �(� − �0) ���� = ���� ���� ���2� + ���2� = 1 SOH CAH TOA � = � = ∆� ∆� � = �� ������ �2 = (� − ℎ) 2 + (� − �)2 �(�) = �0� �� �2 = �2 + � 2 − 2�� ���� ���� � = ����
- 9. � = ���� � � − �0 = �(� − �0) �(�) = �(� − ℎ) 2 + � Running head: HOOSIER MEDIA GROUP 6 HOOSIER MEDIA GROUP Hoosier Media Group Hoosier Media Inc. was founded in 2011 in Pleasantville. The company makes annual revenue of approximately $43,000. Over the past five years, the company has experienced significant decline in the circulation of print newspaper which prompted the need to lower the firm’s revenues by thirty percent. However, despite accounting for five percent of the total revenues, Hoosier Media had an increase in online revenues. In order to determine the best techniques of enhancing the organization’s operations, this paper focuses on the comprehensive analysis of both external and internal factors affecting the company.
- 10. Political factors affect both the regulatory policies as well as the laws enacted by parliament to regulate media operations in the country. With the new government in place, there are prospects that laws will be amended, or new laws enacted that may in one way or another impact the operations of Hoosier Media Inc. These could be laws relating to taxes, environmental policies, social laws etc. Critique how well the organization adapts to change There have been economic challenges that Hoosier Media Group has been able to go through by adopting operational polices to deal with the dynamics that have prompted changes within the company in terms of its operations. The company has been able to successfully adapt to changes by leveraging on its strengths to counter the threats initially posed by the economic crisis. Hoosier Media Inc. has also made it her corporate culture to conform to the rules and regulations as set the government to avoid legal issues that may otherwise result in closure of the business (Hess, 2014) This paper analyses how the company has been able to adapt to change by looking at PEST and SWOT analysis and the operations that have ensured the company remains competitive in the industry. The SWOT analysis covers the Strengths, Weakness, Opportunities and Threats. It is an effective tool to use when analyzing performance especially from departmental perspective; the strategies they employ, the threats they face and the opportunities they have to better their processes (Brooks, 2014). Discuss the primary internal organizational considerations. The SWOT analysis is categorized into internal strategic factors and external strategic factors. In regard to internal strategic factors, the paper discusses the strengths and weaknesses within the organizations. External factors on the other hand include opportunist and the threats faced by the company.
- 11. Strengths The company not only enjoys a highly skilled labor force but also has managed to retain her staff. There are training programs and career development resources the company uses to build its labor force. This has enabled the company to develop a loyal employee support base that is motivated to give their best effort in the best interest of the company. The other strength is the outstanding performance of Hoosier Media Group in the market. It has been successful in entering new markets which has placed it in a good competitive position. The new ventures have not only resulted in increased revenues for the firm but also narrowed down the risk level within the market in which it operates. The strong free flow cash has provided Hoosier Media Group with resources it needs to expand. Weaknesses There is a weakness in the time the firm takes to adopt new technologies. Hoosier Media Inc. needs to invest more in new technology to help improve the quality of the production. This gap allows competitors to easily penetrate the market because they have a loophole to exploit. The company has not properly defined product positioning and selling position and this has resulted in segment attack by rival firms. It is also important to point out that the firm’s growth in the long term is significantly being impacted by high inventory which forces the company to invest more money in the channel (Nason, 2018). Discuss the primary external organization considerations. Opportunities Hoosier Media Group, following the huge investment it made on online platforms, is establishing a new customer base on online platforms and channels. The new market has significantly
- 12. contributed to the revenues generated and through data analytics the company can leverage of the new market by ensuring it meets the needs of its customers with the intent of maximizing on subscription and returns. With the improved economy after the turbulent financial times in the past couple of years, Hoosier Media Group can take this opportunity to capture new markets and consolidate a larger customer base. Threats The market has become competitive due to the growing strength of local distributors working for rival firms. This has a threat as it seeks to lower the market share of Hoosier Media Group. Also, competitors are adopting the latest technologies that are efficient and effective hence disrupting the market and increasing risks (Qureshi, Aziz, and Mian, 2017). References Brooks, G., Heffner, A., & Henderson, D. (2014). A SWOT analysis of competitive knowledge from social media for a small start-up business. The Review of Business Information Systems (Online), 18(1), 23. Hess, T. (2014). What is a media company? A reconceptualization for the online world. International Journal on Media Management, 16(1), 3-8. Nason, R. S., & Wiklund, J. (2018). An assessment of resource- based theorizing on firm growth and suggestions for the future. Journal of Management, 44(1), 32-60. Qureshi, M. S., Aziz, N., & Mian, S. A. (2017). How marketing capabilities shape entrepreneurial firm’s performance? Evidence from new technology-based firms in turkey. Journal of Global Entrepreneurship Research, 7(1), 15.
- 13. NAME: PART I PART II 1a 1a 6a 1b 1b 6b 2a 1c 6c 2b 2a 6d 3a 2b 7a 3b 2c 3c 2d 7b 4a 2e <graph> 4b 3a 5a 3b 7c 5b 3c 8a 6a 3d <graph> 8b 6b 4a 7a 4b 4c