Pre-Calculus homework
MATH 115 QUIZ 3 November, 2019 Instructor: I. Izmirli
NAME: _______________________________
I have completed this assignment myself, working independently and not consulting anyone except the instructor.
INSTRUCTIONS
· The quiz is worth 100 points. There are 10 problems.
· Each problem is worth 10 points
· 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 no later than this Sunday.
· Show work/explanation. Answers without any work may earn little, if any, credit. You may type or write your work in your copy of the quiz, or if you prefer, create a document containing your work. Scanned work is acceptable also. In your document, be sure to include your name and the assertion of independence of work.
· General quiz tips and instructions for submitting work are posted in the Quizzes module.
· If you have any questions, please contact me by e-mail.
1.
(a) Let State the corresponding exponential form of this logarithmic equation.
(b) Determine the numerical value of in simplest form.
2. Use an appropriate change of base formula to approximate to the nearest hundredth.
3. Expand and simplify as much as possible. Assume all quantities represent positive real numbers.
4. Use the properties of logarithms to write the expression as a single logarithm and, if possible, simplify.
(1/5) log4 (x) – log4 (y) – 2 log4 (z)
5. Solve:
6. Solve: log (25x2 – 25) – log(x – 1) = 2
7. The home-ownership rate is the percentage of households that are owner-occupied. Based on data of U.S. home-ownership rates in the second half of the twentieth century, the following logarithmic model was determined:
h(t) = 397 ln(t) 2955
where t = year and h(t) = home-ownership rate, in percent. Using the model, what was the home-ownership rate in 1990, to the nearest tenth of a percent?
8. A cup of hot coffee was placed in a room maintained at a constant temperature of 69 degrees, and the coffee temperature was recorded periodically.
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Using exponential regression with the data set, the following temperature model was produced:
C(t) = 69 + 89.976 e 0.023 t
where t = Time Elapsed (minutes)
and C(t) = Coffee Temperature (in degrees) at time t.
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(a) Use the temperature model to estimate the coffee temperature C when 12 minutes have elapsed. Report your estimated temperature to the nearest tenth of a degree.
(b) Suppose the coffee temperature C is 150 degrees. Solve an appropriate equation for t to determine how much time has elapsed. Report your answer to the nearest tenth of a minute.
(c) Briefly describe what happens to the coffee temperature C(t) as the elapsed time t becomes larger and larger. Is this a realistic description of the behavior of the actual coffee temperature?
9.
(a) For the angle 268°, what is the associated quadrant?
(b) For the angle , what is the associated quadrant?
10.
(a) Convert the angle 225° from degree measure into radian measure.
(b) Convert to degree measure.