Math Quiz
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Math107QuizSpring2020OL4HM.docxMath 107 Quiz 5 Page 2
Math 107 Quiz 5 Instructor:
Your Name__________
Instructions:
· The quiz is worth 100 points and there is an extra credit opportunity at the end. There are 10 problems.
· This quiz is open book and open notes . This means that you may refer to your textbook, notes, and online classroom materials, but you must work independently and may not consult anyone (and confirm this with your submission). You may take as much time as you wish, provided you turn in your quiz by the deadline posted in the course schedule of the syllabus.
· Enter your answers and work using one of these methods:
· Type your answers and work directly in the quiz document, using Microsoft Word. Use the equation editor to enter mathematical expressions. Submit your quiz as a .DOCX file. If you use a different program to complete your quiz, you must convert the file to .DOCX or .PDF.
· Print out the quiz and hand write your answers and work on the printed pages. Scan or take an image of each page and submit the pages as .PDF or .JPG files.
· Regardless of the method you use, you must use this quiz file to enter your answers and work; other formats (such as writing solutions on scratch paper) will not be graded.
· If you have any questions, please contact me by e-mail ([email protected]).
Read the rubric expectations below BEFORE you start working on the quiz.
For each item on the quiz not requiring work to be shown (ex: multiple choice / short answer):
· The answer is clearly stated.
· The answer is correct.
For each item on the quiz requiring work or explanation to be shown:
· Work is presented in a well-organized, legible manner.
· Work includes appropriate explanations, using mathematical techniques learned within the scope of the course.
· Work includes appropriate visual representations (graphs, tables, etc.)
· The results of problem-solving are interpreted correctly.
· Correct mathematical notation and terminology are employed. Correct grammar and spelling are employed.
· The final answer is clearly stated.
· In the case of a word problem, the final answer is stated in a sentence, interpreting the mathematical work in the context of the application, with appropriate units of measurement.
· The final answer is correct.
· Partial credit may be awarded, based on the percentage of correct work shown. No credit is awarded without work shown.
Our textbook is full of good models of work shown correctly. If you have questions about showing work, please ask.
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1) (4 points) Which of the following graphs represent a one-to-one function? There may be more than one graph that qualifies. ______________________ No work required.
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2) (6 points) The growth of an oak tree can be modeled by the logarithmic function , where t is the age of the tree in years. Note that “ln” refers to the natural logarithmic function. Work optional.
a) To the nearest tenth of a foot, how tall is the oak tree at age 5 years?
b) To the nearest tenth of a foot, how tall is the oak tree at age 25 years?
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3) (4 points) Convert to a logarithmic equation: . Choose the correct answer below. No work required.
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4) (8 points) Solve the equation. Check all proposed solutions. Show work for the solution and check, and state your final conclusion. Work required.
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5) (8 points)
a) = ___________ Fill in the blank. No work required.
b) Convert to an exponential equation . No work required.
c) Determine the numerical value of , in simplest form. Work optional.
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6) (10 points) Let and
a) Find the composite function and simplify the result. Work required.
b) Find Work required. |
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7) (16 points) Given the function
a) Find , the inverse function of f. Work required.
b) State the domain of . No work required.
c) State the domain of f. No work required.
d) Find . Work required.
e) What is , where the number in the blank is your answer from part d). Work or explanation required.
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8) (14 points) Given the function .
a) Which of the following describes how the graph of f can be obtained from the graph of ? No work required.
i) Shift the graph of to the right by 1 unit and down by 3 units ii) Shift the graph of to the left by 1 unit and down by 3 units iii) Shift the graph of to the right by 1 and up by 3 units iv) Reflect the graph of to the left by 1 and up by 3 units
b) State the domain of f. No work required.
c) State the range of f. No work required.
d) State the horizontal asymptote. No work required.
e) State the y-intercept. Round your answer to the nearest hundredth. No work required.
f) Which is the graph of f? No work required.
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9) (20 points) The temperature in a city can be modeled by the quadratic polynomial , where y is the temperature in degrees and where t is the hour since midnight (for example, t = 7 is 7 am and t = 13 is 1 pm.
a) Estimate the temperature at 9:30 am, to the nearest tenth of a degree. Work optional.
b) Use algebraic methods to find the time of the maximum temperature. Report the time to the nearest quarter hour (for example, t = 18.25 is 6:15 pm). Work required.
c) Use algebraic methods to find the maximum temperature predicted by the quadratic model, rounded to the nearest tenth of a degree. Work required.
d) Use algebraic methods to estimate the time(s) when the temperature is 60 degrees. Report the time to the nearest quarter hour (for example, t = 18.25 is 6:15 pm). Work required.
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10) (10 points) A hot bowl of soup cools according to Newton’s Law of Cooling so that its temperature at time t (in minutes) is given by the exponential function
a) Find the temperature of the soup after 35 minutes has elapsed, rounded to the nearest tenth of a degree. Work required.
b) Suppose the temperature of the soup is 85 degrees. Write the equation you would use to find the time when the temperature is 85 degrees. No work required.
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EXTRA CREDIT (6 points) Work required.
Use algebraic methods to solve the equation you wrote for Question 10 part b). Round your answer to the nearest tenth of a minute. Interpret your answer in the context of the soup application. |
End of quiz
When you have completed your quiz, you must sign (or type) your name below the following honor statement. Without this signed statement you will receive a zero.
I have completed this quiz myself, working independently and not consulting anyone except the instructor. I have neither given nor received help on this quiz.
Name: _______________________________ Date: _______________________________
