Ebonys Bank Balance Algebra Worksheet

Math | Graded Assignment | Unit Test, Part 2 | Bivariate DataName:
Date:
Graded Assignment
Unit Test, Part 2: Bivariate Data
Answer the questions below. When you are finished, submit this test to your teacher for full credit.
Total score: ____ of 15 points
(Score for Question 1: ___ of 5 points)
1.
The table shows the minimum wage rates for the United States during different years.
Year
1978
1979
1980
1990
1991
1996
1997
2007
2008
2009
Minimum hourly wage ($)
2.65
2.90
3.35
3.80
4.25
4.75
5.15
5.85
6.55
7.25
(a) Write the least squares regression equation that models the data. Let x = time in years since
1900 and let y = minimum hourly wage.
(b) Use the equation to estimate the minimum hourly wage of a U.S. worker in 2025. Show your
work.
Answer:
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Math | Graded Assignment | Unit Test, Part 2 | Bivariate Data
(Score for Question 2: ___ of 5 points)
2. The table shows the soil density of several soil samples at different depths.
Depth (m)
Soil density (
mg/cm3 )
1
5
6
8
10
12
14
21
23
24
28
1045
1063
1102
1140
1191
1232
1249
1254
1265
1268
1273
(a) Write the quadratic regression equation that models the data. Let x = depth below the surface
and let y = soil density.
(b) Use the equation to estimate the soil density of a sample at a depth of 20 m. Show your work.
Answer:
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Math | Graded Assignment | Unit Test, Part 2 | Bivariate Data
(Score for Question 3: ___ of 5 points)
3. Jackson relies on his customers to tell their friends about his business. His business grows as each customer
continues to tell others about his or her experience and they in turn tell others as well.
The table shows the number of people who have recommended Jackson’s business for different days after it
first opens.
Time (days), x
3
4
7
10
12
13
17
18
21
27
30
Number of personal recommendations, y
12
14
18
23
28
31
46
50
67
118
157
(a) Write the exponential regression equation that models the data.
(b) Use the equation to estimate the number of personal recommendations 60 days after Jackson
opens his business. Show your work.
Answer:
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Math | Extended Problems | Function Applications
Name:
Date:
Extended Problems
Function Applications
Solve the problems. When you have finished, submit this assignment to your teacher by the due date for full
credit.
Total score: ____ of 15 points
B (d )
The amount in Ebony’s bank account
is a function of the number of days d since she opened the account.
The graph shows segments representing her day-by-day bank balance. Although there are no labeled tick marks
on the graph, you can answer the questions by using the additional given information as well as your general
knowledge of graphs of functions.
(Score for Question 1: ___ of 4 points)
1. Ebony kept her bank account open for only 3 weeks, and the graph shows the entire 3 weeks. During that
time, her greatest balance was $400.
(a) Give the domain and range of the function.
B (0 )
(b) Give an estimate to the nearest hundreds for
. Explain how you determined your estimate and
B (0 )
tell what
means in context of the situation.
(c) Ebony’s bank balance first reached $0 on Day 12. How would you show that information in function
notation?
(d) Ebony’s bank balance remained at $0 from Day 12 through Day 15. As you count segments from the
left, which segment on the graph1, 2, 3, 4, 5, or 6 represents that information? Explain how you know.
Answer:
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Math | Extended Problems | Function Applications
(Score for Question 2: ___ of 6 points)
2. Ebony’s bank balance first reached $400 on Day 4. The last day her balance was $400 was Day 8.
(a) Determine
(b) Estimate
B (5 ), B (6 ), and B (7 )
B (1), B (2 ), and B (3 )
. Explain how you determined these amounts.
. Explain how you determined these amounts.
(c) Jade said that the amount of money Ebony took out of her account each day between Day 8 and Day
12 was the same amount of money she put into her account each day between Day 0 and Day 4.
Recall that Day 12 is when the balance first reached $0. Without doing any calculations, how could
you show Jade why that cannot be true?
Answer:
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Math | Extended Problems | Function Applications
(Score for Question 3: ___ of 5 points)
3. On Day 16, Ebony deposited $100 into her account. On each day after Day 16, segment 5, Ebony made a
deposit, and those deposits were equal to each other.
(a) Explain how you can determine, just by looking at the graph, whether the amounts she deposited
after Day 16 were each less than $100, $100, or more than $100.
B (21)
(b) Use the graph to estimate
in hundreds. Explain how you determined this estimate. Then show
how you can estimate the amount of money Ebony deposited into her account each day after Day 16.
Answer:
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