Math quiz 7 | Mathematics homework help

1. (5 pts) Which of these graphs represent a one-to-one function? Answer(s): ____________

(no explanation required.)  (There may be more than one graph that qualifies.)

 

 

 

2. (5 pts)  Convert to a logarithmic equation: 7x = 2401.      (no explanation required)      2. ______

     

      A.    

 

      B.   

 

      C.    

 

      D.    

 

 

 

 

3. (10 pts) Based on data about the growth of a variety of ornamental cherry trees, the following logarithmic model about these trees was determined:

 

               h(t) = 6.47 ln(t) + 2.83,  where  t = age of tree in years and h (t) = height of tree, in feet.   

                                                              (Note that “ln” refers to the natural log function)  (explanation optional)

Using the model,

(a) At age 3 years, how tall is this type of ornamental cherry tree, to the nearest tenth of a foot?

 

 

 

 

 

(b) At age 12 years, how tall is this type of ornamental cherry tree, to the nearest tenth of a foot?

 

 

 

 

 

 

 

 

 

 

 

 

4. (5 pts) Solve the equation. Check all proposed solutions. Show work in solving and in checking, and state your final conclusion.

       

                   

 

5. (10 pts) 

         (a)       _______  (fill in the blank)

 

         (b)   Let   State the exponential form of the equation.

 

 

 

         (c)    Determine the numerical value of , in simplest form. Work optional.

 

 

 

 

 

 

 

 

6.  (10 pts)  Let  f (x) = 2x2x – 10 and  g(x) = 3x + 1

 

 (a) Find the composite function  and simplify the results. Show work.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(b) Find . Show work.

 

7. (15 pts)  Let         

 

      (a)  Find 1 , the inverse function of fShow work.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(b) What is the domain of f ? What is the domain of the inverse function?

 

 

 

 

 

 

 

(c) What is f (2) ?           f (2) = ______                                   work/explanation optional

 

 

 

 

 

 

(d) What is 1( ____ ), where the number in the blank is your answer from part (c)?    work/explanation optional

 

8. (15 pts) Let f(x) = e x – 1  + 4.                                                                                     

 

Answers can be stated without additional work/explanation.

 

      (a) Which describes how the graph of f can be obtained from the graph of y = ex ?    Choice: ________

 

            A.     Shift the graph of  y = ex  to the left by 1 unit and up by 4 units.

            B.     Shift the graph of  y = ex  to the right by 1 unit and up by 4 units.

            C.     Reflect the graph of  y = ex  across the x-axis and shift up by 4 units.

            D.     Reflect the graph of  y = ex  across the y-axis and shift up by 4 units.

 

      (b) What is the domain of f ?

 

 

 

      (c) What is the range of f ?

 

 

 

      (d) What is the horizontal asymptote?

 

 

 

      (e) What is the y-intercept?  State the approximation to 2 decimal places (i.e., the nearest hundredth).

 

 

 

 

      (f) Which is the graph of f ?     

 

              GRAPH A                                  GRAPH B                            GRAPH C                             GRAPH D

e1.gife3.gife2.gife4.gif

 

 

NONLINEAR MODELS – For the latter part of the quiz, we will explore some nonlinear models.

 

9. (15  pts)   QUADRATIC REGRESSION  

Data: On a particular summer day, the outdoor temperature was recorded at 8 times of the day, and the following table was compiled. A scatterplot was produced and the parabola of best fit was determined.

 

t = Time of day (hour)

y = Outdoor

Temperature (degrees F.)

7

52

9

67

11

73

13

76

14

78

17

79

20

76

23

61

 

 

Quadratic Polynomial of Best Fit:

      y = 0.3476t2 + 10.948t 6.0778  where t = Time of day (hour) and y = Temperature (in degrees)

 

REMARKS: The times are the hours since midnight. For instance, 7 means 7 am, and 13 means 1 pm.

 

(a) Using algebraic techniques we have learned, find themaximum temperaturepredicted by the quadratic model and find thetime when it occurred. Report the time to the nearest quarter hour (i.e., __:00 or __:15 or __:30 or __:45). (For instance, a time of 18.25 hours is reported as 6:15 pm.) Report the maximum temperature to the nearest tenth of a degree. Show algebraic work.

 

 

 

 

 

 

 

 

 

 

 

 

(b) Use the quadratic polynomial to estimate the outdoor temperature at 7:30 am, to the nearest tenth of a degree. (work optional)

 

 

(c)Use the quadratic polynomial y = 0.3476t2 + 10.948t 6.0778  together with algebra toestimate the time(s) of day when the outdoor temperature  y was 75 degrees.

That is, solve the quadratic equation 75 = 0.3476t2 + 10.948t 6.0778  .

Show algebraic work in solving. State your results clearly; report the time(s) to the nearest quarter hour. 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

10. (10 pts)    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. 

 

t = Time Elapsed

(minutes)

C = Coffee

Temperature (degrees F.)

0

166.0

10

140.5

20

125.2

30

110.3

40

104.5

50

98.4

60

93.9

TABLE 1

REMARKS:

Common sense tells us that the coffee will be cooling off and its temperature will decrease and approach the ambient temperature of the room, 69 degrees.

 

So, the temperature difference between the coffee temperature and the room temperature will decrease to 0.

 

We will fit the temperature difference data (Table 2) to an exponential curve of the form y=Aebt.  

 

Notice that as tgets large, ywill get closer and closer to 0, which is what the temperature difference will do.  

So, we want to analyze the data wheret= time elapsed andy=C 69, the temperature difference between the coffee temperature and the room temperature.

 

TABLE 2

t  = Time Elapsed (minutes)

y= C 69 Temperature

Difference

(degrees F.)

0

97.0

10

71.5

20

56.2

30

41.3

40

35.5

50

29.4

60

24.9

 

 

 

 

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

      y = 89.976 e 0.023t  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) Sincey=C 69, we have coffee temperatureC=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.

 

(c)Suppose the coffee temperature C is 100 degrees.Theny=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).

 

 

Get 20% Discount on This Paper
Pages (550 words)
Approximate price: -

Try it now!

Get 20% Discount on This Paper

We'll send you the first draft for approval by at
Total price:
$0.00

How it works?

Follow these simple steps to get your paper done

Place your order

Fill in the order form and provide all details of your assignment.

Proceed with the payment

Choose the payment system that suits you most.

Receive the final file

Once your paper is ready, we will email it to you.

Our Services

Academic Solvers has put together a group of highly qualified writers with a wide range of expertise in the online writing community. Our goal is to become your one-stop shop for all academic and online writing needs. Take a look at our fantastic service below!

Editing

Research Paper Editing

At Academic SolversEditing your research paper could prove to be difficult especially amidst the tight schedules that students have. At academicsolvers.net, we offer research paper editing services. The services include proofreading and use of online platforms such as Grammarly and Turnitin to address any concerns that may arise within the paper. Get our services and you will have satisfactory results.

Research Paper

Custom Research Paper

Writing a research paper could be quite hectic especially if it is your first time. Identifying the research topic, finding the references and interpreting information could pose significant challenges. However, this should not be issues of concern anymore. At academicsolvers.net, we offer solutions to research papers. We deliver plagiarism free and quality research papers that are customized to suit your needs.

Editing

Online Proofreading

Despite writing expertise and skills, you are never guaranteed of error free papers. Academic solvers’ online proofreading services leaves no mistake unaddressed. We go through your paper using a variety of online tools that help to ensure that we edit your paper and make it error free. We have collected a group of experts hence can guarantee quality proofreading services.

Coursework

Cheap Research Papers

Do you have difficulties writing your research paper? Are you afraid of the cost of hiring a professional to write your research papers? Worry no more. At academicsolvers.net we address both of your problems. We are equipped with a large number of professional writers. Second, we offer our research paper writing services at cheap prices that are largely affordable. Don’t miss this chance. Order our cheap research papers today.

Coursework

College Assignment

College assignment could be one of the biggest challenges to students especially working with tight schedules. Academicsolvers.net acts to bridge this gap existing between getting satisfactory grades and meeting deadlines. Our college assignment professionals provide students with quality, plagiarism free and confidential assignment help that helps them to achieve desired grades and outcomes.

Coursework

Essay Help

Essays are some of the most critical elements in the academic life of a student. At academic solvers we prioritize providing quality essays. As such, our professional ensure that they address issues of grammar, structure and plagiarism to provide essays that meet the need of the client. Here, we focus on developing content that aims at addressing the subject in question through the expertise of our professional and experienced writers. Try our services and we guarantee succes.