Name: _____________________________________
Period: _____________
Chapter #5 Equations of Linear Functions
Date: ______________
Homework Packet #13
Days 11-14
Day # 11 Modeling Linear Functions
(Questions #1-4): Maria charges $15 for every 2 hours that she babysits. Answer the following questions based
on this information.
1. How much would Maria charge for working for 5 hours?
2. Fill out the table below for the amount that Maria makes as she babysits.
3. Graph the relationship on the grid provided.
4. Write an equation for the amount, a, that Maria makes as a function of the number of hours, h, that she babysits. Keep
in mind that Maria will make $0 for babysitting for 0 hours.
(Questions #5-7): The population of deer in a park is growing over the years. The table below gives the population found
in a survey by local wildlife officials.
5. If t stands for the number of
years since 2000, write an equation
for the deer population, p, as a
function of t.
6. What does your model predict
the deer population to be in the
year 2014?
7. In what year will the deer
population reach 500? Round to
the nearest year.
(Questions #8-11): The temperature is falling outside at a steady rate of 4 degrees Fahrenheit every hour. If the
temperature starts at 68 Fahrenheit do the following.
8. Fill out the table below for the outside temperature
during the time it is cooling down.
9. Write a linear equation that relates the Fahrenheit
temperature, F, to the time in hours, t, that it has been
falling.
10. According to your equation, what is the temperature
when t  2.75 hours?
11. If this cooling continues at this constant rate, how
many hours will it take for the temperature to reach the
freezing point of water? Show your work.
(Questions #12-13): In 1997, about 2.6 million girls competed in high school sports. The number of girls competing in
high school sports has increased by an average of 0.06 million per year since 1997.
12. Write a linear equation to find the number of girls in
high school sports.
13. Estimate the number of girls competing in 2017.
MIXED REVIEW (Questions #14-17): Find the inverse of each equation.
14. 𝑓(𝑥) = 𝑥 + 4
15. 𝑓(𝑥) = 4𝑥 + 4
1
16. 𝑓(𝑥) = 4 𝑥 + 1
1
17. 𝑓(𝑥) = 4 𝑥 − 1
2
Day # 12 Recursive Formulas
1. Rondell has saved $75 toward a new stereo system for his car. He plans to save $10 each week for the next
few weeks. Write an explicit and recursively-defined function to model the situation provided.
2. Ana is driving from her home in Miami, Florida, to her grandmother’s house in New York City. On the first
day, she will travel 240 miles to Orlando, Florida, to pick up her cousin to travel with her. Then, they will
travel 350 miles each day. Write an explicit and recursively-defined function to model the situation
provided.
3. A rental company charges $8 per hour for a mountain bike plus a $5 fee for a helmet. Write an explicit and
recursively-defined function to model the situation provided.
4. For Illinois residents, the average tuition at Chicago State University is $175 per credit hour. There is also a
set fee of $218 per year. Write an explicit and recursively-defined function to model the situation provided.
3
MIXED REVIEW:
(Questions #5-7): Find the slope that connects the given points.
5. (-4, 7) and (-6, -4)
6. (19, 3) (20, 3)
7. (19, -2) and (-11, 10)
(Questions #8-9): Write the equation of the line in slope-intercept form through the given point and the given
slope.
8. through (1, 2), slope = 7
9. through (3, -1), slope = -1
(Questions #10-11): State the slope and y-intercept of each.
10. x = -3
11. 2𝑥 + 𝑦 = 4
4
Day # 13 Arithmetic Sequences
(Questions #1-4): For each of the following sequences, determine if it is arithmetic based on the information given. If it is
arithmetic, fill in the missing blank. If it is not, explain why it isn’t.
1.
5, 9, 13, _________, 21, 25
2.
5, 10, 20, 40, __________, 160
3.
7, 4, 1, __________, 5 , 8
4.
64, 16, 4, __________, 4 , 16
5. The fourth term (𝑎4 ) of an arithmetic sequence is 8. If
the common difference is 2, what is the first term?
7. Write an equation for:
-12, -8, -4, 0, …
1
1
6. The common difference of an arithmetic sequence is
-5. If 𝑎12 is 22, what is 𝑎1 ?
8. Write an equation for:
-11, -15, -19, -23, …
9. Find the 15th term of 3, -10, -23, -36, …
5
MIXED REVIEW:
(Questions #10-11): COMPUTERS The table shows the percent of Americans with a broadband connection at
home in a recent year.
10. Find an equation for the regression line and describe the
correlation coefficient (strength and direction). Round to the
nearest hundredth.
11. Use the linear regression equation to estimate the
percentage of 60-year-olds with broadband at home. Round to
the nearest percent.
(Questions #12-13): Graph each equation the grid provided. Show all work. Be sure to use a straight edge and
label each graph.
1
12. 𝑦 = − 3 𝑥 + 3
13. 6𝑥 + 5𝑦 = 20
(Questions #14-15): State the slope and y-intercept of each.
14. y = 4
15. 10𝑥 − 3𝑦 = 15
6
Day # 14 Applying Arithmetic Sequences
(Question #1-4): 12, -1, -14, -27,…
1. Is it an arithmetic sequence? Explain your answer.
2. Write the explicit formula.
3. Write the recursive formula.
4. Find the 8th term using one of these formulas.
(Questions #5-6): Consider the sequence 13, 24, 35, …
5. Write an explicit formula for the sequence in
terms of n.
6. Using your formula, find the 40th term.
(Questions #7-8): Given the following sequences, write a recursive formula and an explicit formula for an.
7. 25, 35, 45, 55, …
8. 29, 20, 11, 2, …
7
9. Find the first five terms of the sequence whose recursive
formula is:
𝑎1 = 13 and 𝑎𝑛 = −2𝑎𝑛−1 − 3 if 𝑛 ≥ 2.
10. A landscaper is building a brick patio. Part of the patio
includes a pattern constructed from triangles. The 2 nd row has
13 bricks and the 3rd row has 11 bricks. Write an explicit and
recursively-defined function to model the situation provided.
MIXED REVIEW
(Questions #11-13): PHYSICAL FITNESS The table below shows the percentage of seventh grade students in public school who
have met all six of California’s physical fitness standards each year since 2002. (Hint: this means to change what you put in for L1 to
“years since 2002”)
11. Find the regression equation.
Round to the nearest hundredth.
12. Describe the correlation
coefficient (strength and direction).
Round to the nearest thousandth.
13. In 2008, what percentage of 7th
graders met the physical fitness
standards of California? Leave your
answer to the nearest tenth of a
percent.
(Questions #14-15): Write the equation of the line in slope-intercept form through the given point and the given slope.
5
14. through (3, 5), slope = 3
15. through (2, 5), slope = undefined
8
Homework Packet #13 Answers
Day #11 Modeling Linear Functions
Day #13 Arithmetic Sequences
1. 37.50
2. 30, 45, 60, 75, 90
3. Correct graph
4. a (h) = 7.50h
5. p (t) = 16t + 168
6. 392
7. 2021
8. 68, 64, 60, 56
9. F = -4t + 68
10. 57
11. 9
12. G = 0.06n + 2.6
13. 3.8
1. yes, d = 4; 17
2. doesn’t have a common difference
3. yes, d = -3; -2
4. doesn’t have a common difference
5. 2
6. 77
7. an = 4n – 16
8. an = -4n – 7
9. -179
Mixed Review
14. 𝑓 −1 (𝑥) = 𝑥 − 4
1
15. 𝑓 −1 (𝑥) = 4 𝑥 − 1
16. 𝑓 −1 (𝑥) = 4𝑥 − 4
17. 𝑓 −1 (𝑥) = 4𝑥 + 4
Mixed Review
10. y = -.34x + 49.48, r = -.88
strong, negative correlation
11. 29%
1
12. Correct graph, m = − 3, b (0, 3)
6
13. Correct graph, m = − , b (0, 4)
5
14. m = 0, b: (0, 4)
10
15. m = , b: (0, -5)
3
Day #12 Recursive Formulas
Day #14 Applying Arithmetic Sequences
1. Explicit: y = 10x + 75
Recursive: 𝑎1 = 75; 𝑎𝑛+1 = 𝑎𝑛 + 10
2. Explicit: y = 350x + 240
Recursive: 𝑎1 = 240; 𝑎𝑛+1 = 𝑎𝑛 + 350
3. Explicit: y = 8x + 5
Recursive: 𝑎1 = 5; 𝑎𝑛+1 = 𝑎𝑛 + 8
4. Explicit: y = 175x + 218
Recursive: 𝑎1 = 218; 𝑎𝑛+1 = 𝑎𝑛 + 175
1. Yes, common difference of -13
2. y = -13n + 25
3. 𝑎1 = 12; 𝑎𝑛+1 = 𝑎𝑛 − 13
4. 𝑎8 = −79
5. 𝑎𝑛 = 11𝑛 + 2
6. 𝑎40 = 442
7. Explicit: 𝑎𝑛 = 10𝑛 + 15
Recursive: 𝑎1 = 25; 𝑎𝑛 = 𝑎𝑛−1 + 10
8. Explicit: 𝑎𝑛 = −9𝑛 + 38
Recursive: 𝑎1 = 29; 𝑎𝑛 = 𝑎𝑛−1 − 9
9. 13, -29, 55, -113, 223
10. Explicit: y = -2n + 17
Recursive: 𝑎1 = 15; 𝑎𝑛−1 = 𝑎𝑛 − 2
Mixed Review
11
5. 2
6. 0
2
7. − 5
8. 𝑦 = 7𝑥 − 5
9. 𝑦 = −𝑥 + 2
10. m = undefined, b: none
11. m = -2, b: (0, 4)
Mixed Review
11.
12.
13.
14.
15.
y = 3.14x + 29.06
strong, positive correlation
47.9%
5
𝑦 = 3𝑥
x=2
9