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#### Project 3 Evaluation 33 Precalculus: Analytic Geometry & Algebra (MTHH 043 059) Be sure to include ALL pages of this project (including the directions and the assignment) when you send the project to your teacher for grading

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Project 3 Evaluation 33 Precalculus: Analytic Geometry & Algebra (MTHH 043 059) Be sure to include ALL pages of this project (including the directions and the assignment) when you send the project to your teacher for grading. Don’t forget to put your name and I.D. number at the top of this page! This project will count for 10% of your overall grade for this course. Be sure to read all the instructions and assemble all the necessary materials before you begin. You will need to print this document and complete it on paper. Feel free to attach extra pages if you need them. To earn full credit, you must justify your solutions by showing your work. When you have completed this project you may submit it electronically through the online course management system by scanning the pages into either .pdf (Portable Document Format), or .doc (Microsoft Word document) format. If you scan your project as images, embed them in a Word document in .gif image format. Using .gif images that are smaller than 8 x 10 inches, or 600 x 800 pixels, will help ensure that the project is small enough to upload. Make sure your pages are legible before you upload them. Be sure to show all your work for full credit. 1. Sketch the graph of f(x) ? 3? x . Indicate the domain and range. 2. Sketch the graph of g(x) ? log2 (x ? 2) . Indicate the domain and range. Project 3 MTHH 043 1 as an equivalent logarithmic equation. 8 3 . Rewrite 2?3 ? 4. Rewrite log2 5. Find the solution set of log4 (x ? 3) ? log4 x ? 1 . 1 ? ?2 as an equivalent exponential equation. 4 Set up and simplify the equations for the solutions to the following applied problems. If the solution can be found using the properties of logarithms, complete the solution of the problem. 6. ? ? The growth of a certain bacteria is given by the equation B ? A e4t , where A is the original number of bacteria, t is the time in hours, and B is the number of bacteria present at any time t. If the original number of bacteria is 1000, how many bacteria are present after 2 1 2 hours? 7. The loudness of a sound in decibels is related to the intensity of the sound i , where the ? i ? ? , and i0 is a constant equal to the ? i0 ? function for the loudness is given by L ? i ? ? 10log10 ? minimum sound that can be detected by the human ear. Find the loudness in decibels of a recording of rock music with intensity 10 million times i0 . Project 3 MTHH 043 Use either the substitution method or the elimination method to find the solution set of each system of equations. Sketch the graphs of the systems in problems 8, 9, 10, and 11. 8. 2x – 3y ? –13 – x ? 6y ? 20 9. x ? 4y ? 6 x ? 8y 10. x2 ? y2 ? 9 x2 – y ? 9 Project 3 MTHH 043 11. x ?3 y 2 – x 2 ?1 6 12. x ? –2y 3x ? 2y – 3z ? 4 2x – 2y ? 7z ? 6 Sketch the region defined by each system of inequalities, and find the corner points of the boundary of each region. 13. Project 3 y ? x –3 2x ? y ? 3 MTHH 043 14. x ? 2y x?y ? 9 y ?2 15. Use Cramer's Rule to solve the linear system. x – 2y – z ?1 2x ? y ? 5 x ? y – 3z ? 6 16. For the following system of equations, find the augmented matrix, reduce it to an echelon matrix, and find the solution set. x ? y ? z ?2 x – y – z ?0 2x ? y ? 4 Find the solution set of each equation. 17. 9x ? 3x ? 6 18. log3 (x ? 2) ? 2 Project 3 MTHH 043 x ?3 19. ? 1? ?5? ? ? 20. logx 21. Evaluate the determinant. ? 252x 1 ?3 8 ? 4 6 2? ??1 0 1 ? ? ? ?? 3 5 3 ?? Solve the following applied problem using a system of equations. 22. The sum of three numbers is 35. The second number is twice the first, and the third number is twice the second. What are the numbers? 23. Project 3 Write 3loga 4 ? loga 7 as a single logarithm. MTHH 043 Given: logb 2 ? 0.4, logb 3 ? 0.5, and logb 5 ? 0.6. Use properties of logarithms to find the following values. 24. logb 75 25. logb 0.4 Declaration I know that plagiarism is wrong. Plagiarism is to use another’s work and pretend that it is one’s own. I declare that this is my own work. Signature _________________________________ Student I.D. number ________________ This project can be submitted electronically. Check the Project page in the UNHS online course management system. Project 3 MTHH 043

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