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Crauder et al - Functions and Change 6/e (Homework)

James Finch

Math - College, section 1, Fall 2019

Instructor: Dr. Friendly

Current Score : 10 / 13

Due : Sunday, January 27, 2030 00:00 EST

Last Saved : n/a Saving...  ()

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Question
Points
1 2 3 4 5 6 7
2/2 4/4 1/1 1/1 1/1 1/1 0/3
Total
10/13 (76.9%)

  • Instructions

    Functions and Change: A Modeling Approach to College Algebra, 6th Edition, by Bruce Crauder, Benny Evans, and Alan Noell, published by Cengage Learning, is ideal for all students who take college algebra, whether or not they'll continue on to calculus. Graphing utilities, functions, modeling, real data, applications, and projects develop students' skills and give them the practice they need to master basic mathematics and apply it in future courses and careers. With new material on quadratic functions, additional emphasis on business applications, and new Excel activities, the sixth edition reinforces the authors' focus on connecting math in the real world, promotes mastery of the material, and fosters critical thinking.

    Question 1 contains expression grading that represents an exponential model, where any equivalent form of the expression is accepted.

    Question 2 includes a Watch It and a pull-down for word answers, such as equal or not equal.

    Question 3 exhibits a Master It tutorial and solution for elementary properties of the Richter Scale.

    Question 4 highlights prompts that describe the needed answer format.

    Question 5 demonstrates grading for factored expressions.

    Question 6 contains regression grading that gives tolerance to the regression parameters.

    Question 7 showcases a quadratic regression application that requires expression grading for the first answer blank. This demo assignment allows many submissions and allows you to try another version of the same question for practice wherever the problem has randomized values.

    The answer key and solutions will display after the first submission for demonstration purposes. Instructors can configure these to display after the due date or after a specified number of submissions.

Assignment Submission

For this assignment, you submit answers by question parts. The number of submissions remaining for each question part only changes if you submit or change the answer.

Assignment Scoring

Your last submission is used for your score.

1. 2/2 points  |  Previous Answers CraudColAlg6 4.2.EX.005. My Notes
Question Part
Points
Submissions Used
1 2
1/1 1/1
1/100 1/100
Total
2/2
 
Data from the Statistical Abstract of the United States show that in 1995 there were 56.61 thousand performances in the United States by nonprofit professional theaters. From 1995 through 2007, this number increased on average by about 10% each year.
(a) Let P denote the number of performances, in thousands, and let t denote the time in years since 1995. Make an exponential model for P versus t.
P =
56.61(1.10)t
Correct: Your answer is correct. webMathematica generated answer key


(b) How many performances by nonprofit professional theaters does your model give for 2002? (Round your answer to two decimal places.)
Correct: Your answer is correct. seenKey

110.32

 thousand
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2. 4/4 points  |  Previous Answers CraudColAlg6 4.3.EX.003. My Notes
Question Part
Points
Submissions Used
1 2 3 4
1/1 1/1 1/1 1/1
1/100 1/100 3/100 2/100
Total
4/4
 
Show that the following data are not exponential.
t h(t) t h(t)
0 4.7 3 190.7
1 25.4 4 339.4
2 87.1 5 539.6
Compute the first two ratios. (Round your answers to two decimal places.)
h(1)/h(0) = Correct: Your answer is correct. seenKey

5.40
h(2)/h(1) = Correct: Your answer is correct. seenKey

3.43

These ratios are Correct: Your answer is correct. seenKey

not equal

 and the changes in t are Correct: Your answer is correct. seenKey

equal

 . Therefore h is not an exponential function.

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3. 1/1 points  |  Previous Answers CraudColAlg6 4.5.SB.001.MI. My Notes
Question Part
Points
Submissions Used
1
1/1
3/100
Total
1/1
 
This exercise uses elementary properties of the Richter Scale.

One earthquake reads 4.5 on the Richter scale, and another reads 7.2. How do the two quakes compare? (Round your answer to the nearest whole number.)
The 7.2 earthquake is Correct: Your answer is correct. seenKey

501

 times as powerful as the 4.5 earthquake.


Solution or Explanation
If one earthquake reads 4.5 on the Richter scale and another reads 7.2, then the 7.2 earthquake is
107.2 − 4.5 = 102.7 = 501
 times as powerful as the 4.5 earthquake, rounded to the nearest unit.

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4. 1/1 points  |  Previous Answers CraudColAlg6 A.6.003. My Notes
Question Part
Points
Submissions Used
1
1/1
2/100
Total
1/1
 
This problem provides practice with the basic rules for exponents. Use the law of exponents to simplify the given expression. Write your final answer without using negative exponents. (Simplify your answer completely.)
a2b5a3b−4
a5b
Correct: Your answer is correct. webMathematica generated answer key
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5. 1/1 points  |  Previous Answers CraudColAlg6 A.4.009. My Notes
Question Part
Points
Submissions Used
1
1/1
4/100
Total
1/1
 
Write
x3 − 8
 as a product of a linear factor and a quadratic factor.
(x−2)(x2+2x+4)
Correct: Your answer is correct. webMathematica generated answer key
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6. 1/1 points  |  Previous Answers CraudColAlg6 3.4.EX.001. My Notes
Question Part
Points
Submissions Used
1
1/1
1/100
Total
1/1
 
The table below shows the number A, in millions, of motor vehicle accidents t years after 2004.† Find the equation of the regression line for A as a function of t. (Round regression line parameters to two decimal places.)
A(t) =
10.86−.15t
Correct: Your answer is correct. webMathematica generated answer key
t = years since 2004 A = millions of accidents
0 10.9
1 10.7
2 10.4
3 10.6
4 10.2
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7. 0/3 points  |  Previous Answers CraudColAlg6 5.5.EX.006.MI. My Notes
Question Part
Points
Submissions Used
1 2 3
0/1 0/1 0/1
1/100 1/100 1/100
Total
0/3
 
The side of a cylindrical can full of water springs a leak, and the water begins to stream out. (See the figure below.) The depth H, in inches, of water remaining in the can is a function of the distance D in inches (measured from the base of the can) at which the stream of water strikes the ground. Here is a table of values of D and H.
Distance D
in inches 		Depth H
in inches
0 1.00
1 1.25
2 2.00
3 3.25
4 5.00
(a) Use regression to find a formula for H as a quadratic function of D.
H =
10.86−.15D
Incorrect: Your answer is incorrect. webMathematica generated answer key


(b) When the depth is 4 inches, how far from the base of the can will the water stream strike the ground?
Incorrect: Your answer is incorrect. seenKey

3.46

 inches

(c) When the water stream strikes the ground 5 inches from the base of the can, what is the depth of water in the can?
Incorrect: Your answer is incorrect. seenKey

7.25

 inches


Solution or Explanation
(a) The regression parameters for the quadratic model are calculated in the figure below. We find the quadratic model
H = 0.25D2 + 1.
QuadReg
    y = ax2 + bx + c
a = 0.25
b = 0
c = 1
 		WebAssign Plot


(b) We are given that
H = 4,
 and we want to find D. Thus we want to solve the equation
H(D) = 4
 for D. We do this using the crossing graphs method. (We could use the quadratic formula instead.) From the original table of data we see that the solution lies between
D = 3
 and
D = 4.
 In the figure below we have graphed H and the constant 4 using a horizontal span of 0 to 4 and a vertical span of 0 to 4. We see that the intersection occurs at
D = 3.46.
 Thus the stream will strike the ground 3.46 inches from the base of the can when the depth is 4 inches.

(c) When D = 5 the depth is
H(5) = 0.25 · 52 + 1 = 7.25 inches.

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