Q5

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, some with multiple parts. The problems 9 and 10 carry 15 points each. The other eight problems have total of 72 points. This quiz has extra credit points at the end which is optional work. 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 Tuesday 10/06/2020 by 11:59 PM.

· Show your work. 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 conference.

· If you have any questions, please contact me by e-mail.

Problem # 1: Write inverse of the function below:

Use composition of functions to calculate/show that is correctly obtained:

Hint: Find inverse of the function in part (a) by definition of inverse function.

Problem # 2: Use composition of functions to show that is as given:

Problem # 3: For the one-to-one function

Find

a)

b) Domain and Range for

c) Domain and Range for

Hint: This is simple asymptotic function. One can solve very easily.

Hint: for problem 4 needs you to recall back how to solve exponential and radicals that you studied in intermediate algebra class. You may look at formula sheet as well.

Problem # 5: Find each of the following (You may use calculator; round to 3 decimal places)

Problem # 6: Express as a single logarithm

Problem # 7: Express in terms of sums and differences of logarithms

Hint: Use laws of logarithmic functions.

a)

b)

c)

Hint: Problem 10, part(c) is done operation of the function ‘f’ itself.

9. (14 points) Quadratic regression model: A study was done to compare for an automobile between the speed and mpg(miles per gallon).

Solve following:

(a) Use a graphing utility, for example DESMOS calculator, TI-series calculator or maybe MS Excel.

(b) Go for regression feature in the calculator or MS excel to find/create a model which would be a best fit for the data given above in the table.

(c) Find an approximation of the speed at which mileage will be the greatest.

Hint: The regression model may look as below: +0.746x+13.47 Try using maximum and zoom feature. If you use MS Excel, it will do the best fit for you. It may come out (45,30) for the quadratic equation written above. Show your work to obtain full points.

I will add a sample example in the Resources using MS Excel and another software known as Octave, MATLAB for you to have a look. The above hint is for TI-series calculator. Use quadratic regression feature.

10. (14 points) + (extra credit at the end) EXPONENTIAL REGRESSION

Data: 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, in Table 1. 

Exponential Function of Best Fit (using the data in Table 2):

y = 89.976 e 0.023 t where t = Time Elapsed (minutes) and y = Temperature Difference (in degrees)

(a) Use the exponential function to estimate the temperature difference y when 25 minutes have elapsed. Report your estimated temperature difference to the nearest tenth of a degree. (explanation/work optional)

(b) Since y = C  69, we have coffee temperature C = y + 69. Take your difference estimate from part (a) and add 69 degrees. Interpret the result by filling in the blank:

When 25 minutes have elapsed, the estimated coffee temperature is ________ degrees.

(d) Suppose the coffee temperature C is 100 degrees. Then y = C  69 = ____ degrees is the temperature difference between the coffee and room temperatures.

(d) Consider the equation _____ = 89.976 e 0.023t where the ____ is filled in with your answer from part (c).

EXTRA CREDIT (6 pts):

Show algebraic work to solve this part (d) equation for t, to the nearest tenth. Interpret your results clearly in the context of the coffee application. [Use additional paper if needed]

Temperature Difference between Coffee and Room

y = 89.976e-0.023t R² = 0.9848

Time Elapsed (minutes)

Temperature Difference (degrees)

Instructor Dr. K.S. Altmayer