MAT171 Central Piedmont Community Algebra Words Problem Signature Assignment

Answering and show your working all of these question.

MAT 171 Signature Assignment
This assignment is to be uploaded to Blackboard by Monday, December 3rd. Your grade on this assignment will be composed
of 2 parts. You will be given a mathematical grade based on the accuracy of your answers and interpretations (very much like
a test or quiz). You will also be given a “Critical Core” score, based on the following information and rubric below. The
mathematical grade will count towards 80% of the assignment and the “Critical Core” will count towards 20% of this
assignment. Here is a breakdown for the CRITICAL CORE portion: 1=5pts, 2=10pts, 3=15pts, 4=20pts.
A CRITICAL CORE Education
CPCC recognizes that higher education must provide students with the critical knowledge and skills required for academic,
professional, and personal success. A CRITICAL CORE education refers to the college’s understanding that academic, professional,
and personal success requires student competency in the following areas:
•
•
•
•
Communication
Critical Thinking
Personal Growth and Cultural Literacy
Information Technology and Quantitative Literacy
All curriculum courses offered at the college provide students the opportunity to attain and document proficiency in one of these
areas. This course is aligned with Information Technology and Quantitative Literacy, and as such, will focus on providing students
•
•
The ability to locate, understand, evaluate, and synthesize, information and data in a technological and data-driven
society
Students will apply Quantitative concepts to analyze data
The Signature Rubric that is aligned with this course, and illustrates your expected path of growth in the competency, is provided
below:
COMPETENCY: INFORMATION TECHNOLOGY AND QUANTITATIVE LITERACY
KEY INDICATOR 2: STUDENT APPLIES QUANTITATIVE CONCEPTS TO ANALYZE DATA.
0
Blank
Indicates an
assignment was
not submitted.
Indicates
submission of an
assignment that
does not allow for
sufficient or
appropriate
scoring of skill, for
example, an
assignment that
was plagiarized.
Beginning
1
Uses the
quantitative
analysis of data as
the basis for
drawing unclear
conclusions from
this work.
Emerging
2
Uses the
quantitative
analysis of data
as the basis for
drawing
plausible
conclusions
from this work.
Emerging
3
Uses the
quantitative
analysis of data
as the basis for
drawing
reasonable and
appropriately
qualified
conclusions
from this work.
Proficient
4
Uses the
quantitative analysis
of data as the basis
for drawing
insightful, carefully
qualified
conclusions from
this work.
Table 1**”Reprinted [or excerpted] with permission from Assessing Outcomes and Improving Achievement: Tips and tools for Using Rubrics, edited
by Terrel L. Rhodes. Copyright 2010 by the Association of American Colleges and Universities.”
revised Aug 2017
MAT 171 Signature Assignment
Name: ______________________________
{Blank spaces (white space) left intentionally to provide room for student responses.}
All verbal responses should be written in clear and complete sentences and should be unique (do not
plagiarize from any source, including a classmate). You are being graded on both mathematical and
communication skills. Each question is worth 3.33 points.
I.
Dr. Jones has found that, over the years, 95% of the babies she has delivered weighed x pounds, where
|𝑥 − 8.2| − 1.5 ≤ 0.
(SLO #2)
1. Solve the inequality. Show your work.
2. Interpret the meaning of your answer to part (a) in the context of this problem.
3. How likely (or unlikely) would it be for the next baby Dr. Jones delivers to weigh 6 pounds 5 ounces?
Explain.
II.
Jennifer has a taco stand. She has found that her daily costs can be modeled by 𝐶(𝑥) = 𝑥 2 − 40𝑥 + 610, where
C(x) is the cost, in dollars, to sell x units of tacos.
(SLO #1, 6)
4. If she wants to keep her daily costs at $300, how many units of tacos does she need to sell? Give all
possible answers, rounding off to nearest whole number. Show your work.
5. Which answer to part (a) makes the most sense from Jennifer’s point of view? Explain why.
III.
One model for the ideal body weight, W, for men (in kilograms) is 𝑊 = 50 + 2.3(ℎ − 60), where h represents
height (in inches).
(SLO #5)
6. According to this model, what is the ideal weight of a 6-foot male? Do not round your answer.
7. Rewrite the function in order to express height as a function of weight. Call this function h. Show your
work.
8. Verify that the given function and your function from part (b) are inverses, by showing that
(𝑊 ∘ ℎ)(𝑊) = 𝑊 and that (ℎ ∘ 𝑊)(ℎ) = ℎ.
9. What is the height of a male whose ideal weight is 83 kg? Round to nearest inch.
IV.
An independent home builder’s annual profit, in thousands of dollars, can be modeled by the function
𝑃(𝑥) = 5.152𝑥 3 − 143𝑥 2 + 1102𝑥 − 1673, where x is the number of houses built in a year. His company can
build at most 13 houses in a year.
(SLO #1, 2, 6)
10. Find the y-intercept and explain what it means in this context.
11. Find the x-intercept(s) and explain what they mean in this context.
12. Determine the domain of the function in the context of this problem.
13. How many houses should the builder construct in order to have a profit of at least $400,000?
V.
14. How many houses should the builder construct in order to maximize profit?
The graph below represents the population of insects, in thousands, over a 12 month period beginning in March
2010. Use the graph to answer the questions.
(SLO #3, 6)
15. Explain why an exponential or logarithmic function would not be used to model this graph.
16. What is the minimum possible degree polynomial that can model this graph? Explain.
17. Find the x-intercept(s) and interpret their meaning in this context.
18. When (give name of month and year) was the population at its lowest level?
19. When (give name of month and year) did the population reach its maximum? How many insects where
there at that time?
VI.
The function 𝐶(ℎ) =
2ℎ2 +5ℎ
ℎ 3 +8
models the concentration of a medication in the bloodstream (as a percent) ℎ
hours after its injection into muscle tissue.
(SLO #3, 6)
20. a. Determine the domain of the function in the context of this problem.
b. Find the equation of the vertical asymptote of this function. {Hint: 𝑎3 + 𝑏 3 = (𝑎 + 𝑏)(𝑎2 − 𝑎𝑏 + 𝑏 2 )}
Would this concern a medical professional? Explain.
21. Find the equation of the horizontal asymptote. What does this mean in this context?
22. Find all of the intercepts of C and interpret their meaning in the context of this problem.
23. How many hours after injection does a maximum concentration of the drug occur in the bloodstream?
Round answer to nearest hundredth.
24. Suppose you need to re-administer this injection at the point when the concentration is less than 0.5%.
If the first injection was given at 8:00 am, what time should the next injection be given?
VII.
Kristen invests $5,745 in a bank. The bank pays 6.5% interest compounded monthly.
(SLO #6)
25. How long must she leave the money in the bank for it to double? Round to nearest tenth of a year.
Show your work.
26. How long will it take to triple? Round to nearest tenth of a year. Show your work.
27. Kristen has a choice to invest her money at 6.5% interest compounded monthly for 5 years or invest her
money compounding quarterly at a rate of 6.75% for 5 years. What option would be best for Kristen?
Explain and show your work.
VIII.
At Redbox Mike rents 2 DVD’s and 3 games for a total of $15.50. At the same time John rents 3 DVD’s and 1
game for a total of $12.05.
(SLO #4)
28. Write a system of equations that represents this scenario. Clearly indicate what your variables
represent in the context of the problem.
29. How much money is needed to rent a combination of one game and one DVD? Show your work.
30. Redbox is running a one day special giving the customer 50 cents off per game. Mike’s sister wants to
rent 1 DVD and some games. If she has $8.45 to spend at Redbox, how many games may she rent?
Explain.