ALGEBRA U7 HWK DAY 1 SEQUENCES
1. Given the following sequences, write the next three terms and describe the pattern.
(a) -2, 0, 2, 4, 6, …
(b) -4, -12, -36, -108, …
(c) 1, 4, 9, 16,…
(d) 24, 12, 6, 3, …
11 13 (e) 5, , 6, ,... 2 2
2. Complete the table below and graph the coordinates.
n f(n)
1 3 2 6 3 9 4 12
f(n)=
Using the formula for f(n), find f(60)
3. Given the formula f(n) 4n 1, find the following: a. f(3) b. f(0) c. f(-2)
4. Describe the rate of change described in each table below.
5. In a piggy bank on his dresser, Tom has a total of $2.85 in pennies and quarters. If the number of Tom’s pennies is 5 more than three times the number of quarters, how many pennies and quarters does he have in the piggy bank?
5 2 x 4 x 7 6. Solve for x: 9 9
5x 3y 4 7. Solve the following system: 3x 2y 9 Algebra U7 HWK Day 2 Sequences
For problems 1 – 5
a) tell where the sequence is arithmetic, geometric, or neither b) give a reason for your choice c) write the next two terms (next to original #s)
1) 27, 31, 35, … a) b)
2) 58, 45, 32, … a) b)
3) 100, 90, 81, … a) b)
4) 3, 8, 15, 24, 35, 48, 63, 80, 99, … a) b)
For numbers 5 & 6, answer the following questions:
a. Does the sequence have a common difference or ratio? What is it? b. Is the sequence arithmetic or geometric? c. Write the formula for the function.
5) 6) n f(n)
1 4 2 16 3 64 4 256 7) The following table shows the relationship between the wing span of a plane and the plane’s body length, measured in feet, for Boeing aircrafts. Aircraft Name Wingspan Body Length
707 145.75 152.92
727 108 108
737 93 102.5
757-200 124.83 155.25
767 156.08 159.17
757-300 124.83 178.58
a. Write the linear regression equation, rounding all coefficients to the nearest tenth.
b. State the correlation coefficient to the nearest tenth, and describe the strength of the least squares line.
c. Determine the residual for a Boeing 737 to the nearest tenth.
d. Using the regression equation, predict the wing span of a Boeing airplane with a body length of 125 feet to the nearest hundredth.
e. Using the regression equation, predict the body length of a Boeing airplane with a wingspan of 128.5 feet to the nearest hundredth.
8) If x – 1 represents an odd integer, what represents the next greater odd integer?
(1) x (2) x + 2 (3) x – 3 (4) x + 1
9) Which equation represents a line that is parallel to the line whose equation is 2x – 3y = 9?
2 2 3 3 (1) y x 4 (2) y x 4 (3) y x 4 (4) y x 4 3 3 2 2
ALGEBRA U7 HWK DAY 3 EXPLICIT VS RECURSIVE
Identify the following as either an explicit or a recursive formula. Find the first four terms of each sequence. n 2 1) a 3n 2) a n n n
a 1 1 a 1 2, 3) 4) a n 2a n1 5 a n1 4a n 1
5) Given the sequence: 2, 7, 12, 17, 22,…
a) List the next three terms of the sequence.
b) Write an explicit formula for an.
c) Write a recursive definition for the sequence.
6) Which of the following is an equation that has a zero slope and goes through the point (3, -5)?
(1) x = 3 (3) y = -5
(2) x = -5 (4) y = 3 7) Tina wants to make a rectangular sandbox that has a perimeter of 78 inches . The width is three more than twice the length. Determine the dimensions of the sandbox.
2 8) Graph a line that has a slope of and goes through the point (-6, 1). 3
Write the equation of the line graphed.
9) Which equation below represents an exponential function?
(1) 4x 2 3 19 (3) 3x 7 25
(2) 5x 125 (4) 12 2x 5
ALGEBRA 1 HW 7-4
1. Write the first five terms of each sequence.
a) an = 12 – 3n b) a1 = 1 an = 2an-1 +1 For each of the following sequences in 2-5, determine the following:
a. What type of sequence is it and why? b. Write an explicit formula for the sequence. c. Write a recursive formula for the sequence. d. Find the 12th term of the sequence.
2. 17, 23, 29, 35 … 3. –.125, .5, –2, 8 …
4. Consider the arithmetic sequence 13, 24, 35 …
a. Find an explicit formula for the sequence in terms of n.
b. Find the 40th term.
c. If the nth term is 299, find the value of n. 5. Leslie noticed that the daily number of text messages she received over the course of two months form an arithmetic sequence. If she received 6 texts on the first day of the two months and received an additional 3 more texts each following day, how many texts did she receive on:
a) day 27?
b) day 60?
6. Write the equation of a line that is perpendicular to:
a) y = 4
b) y = 3x – 7
c) 5x – 4y = 16
ALGEBRA 1 HW 7-5
1. $250 is invested at a bank that pays 7% simple interest. Calculate the amount of money in the account after 1 year; 3 years; 7 years; 20 years?
2. $325 is borrowed from a bank that charges 4% interest compounded annually. How much is owed after 1 year; 3 years; 7 years; 20 years? 3. A youth group has a yard sale to raise money for a charity. The group earns $800 but decided to put its money in the bank for a while. Calculate the amount of money the group will have if:
a. Cool Bank pays simple interest at a rate of 4% and the youth group leaves the money in for 3 years.
b. Hot Bank pays compound interest at a rate of 3% and the youth group leaves the money in for 5 years.
c. If the youth group needs the money quickly, which is the better choice? Why?
4. Joseph has $10,000 to invest. He can go to Yankee Bank that pays 5% simple interest or Met Bank that pays 4% interest compounded annually.
# of years Yankee Bank (add P) Met Bank a. Fill in the table for the 14 years.
b. Write a formula for the interest he
will earn after 𝒕 years at
Yankee Bank. c. Is this formula explicit or recursive?
d. Write a formula for the total amount he will have after 𝒕 years at Met Bank.
e. Is this formula explicit or recursive?
f. Is the sequence in the Yankee Bank column arithmetic or geometric? Why?
g. Is the sequence in the Met Bank column arithmetic or geometric? Why?
5. Carly is babysitting at $8 per hour to earn money for a car. So far she has saved $1300. The car that Carly wants to buy costs at least $5440. How many full hours must Keisha still work in order to have enough money to buy the car?
ALGEBRA 1 HW 7-6
1. Chain emails are emails with a message suggesting you will have good luck if you forward the email on to others. Suppose a student started a chain email by sending the message to 3 friends and asking those friends to each send the same email to 3 more friends exactly 1 day after they received it.
a. Write an explicit formula for the sequence that models the number of people who
will receive the email on the 𝑛𝑡ℎ day. (Let the first day be the day the original email was sent.)
Assume everyone who receives the email follows the directions. b. Which day will be the first day that the number of people receiving the email exceeds 100?
c. How many total people will have read the email after one week?
2. Write the first five terms of each sequence.
a) an = –5 – 7n b) a1 = 84 an = 2an-1 – 42
3. Consider this sequence and complete the table. Graph the coordinates from the table.
an f(n)
a1 80
a2 40
a3 20
a4 10 a. What is the name of this type of function?
b. What type of sequence is it? Why?
c. Write the equation of this function as both an explicit and a recursive formula.
d. Find f(12) as a fraction in simplest form.
y 4. Graph: 2x – y 4
x
ALGEBRA 1 HW 7-7
1. In 1995, there were 85 rabbits in Central Park. The population increased by 12% each year. How many rabbits were in Central Park in 2005?
2. The value of an early American coin increases in value at the rate of 6.5% annually. If the purchase price of the coin this year is $1,950, what is the value to the nearest dollar in 15 years? 3. In 1985, there were 285 cell phone subscribers in the small town of Centerville. The number of subscribers increased by 75% per year after 1985. How many cell phone subscribers were in Centerville in 1994?
4. Solve the following system algebraically.
2x + 5y = 2 y = 3x – 20
FOR THIS PROBLEM, # 5 a – f, REFER TO DAY 5 NOTES ON INTEREST!!!
5. Student Friendly Bank pays a simple interest rate of 2.5% per year. Neighborhood Bank pays a compound interest rate of 2.3% per year, compounded yearly.
a. Write an explicit formula S(t) for the sequence that models the balance of the Student
Friendly Bank balance, 𝒕 years after a deposit is left in the account. b. Write an explicit formula N(t) for the sequence that models the balance of the Neighborhood
Bank balance, 𝒕 years after a deposit is left in the account.
c. Which bank will provide the largest balance if you plan to invest $10,000 for:
i) 4 years?
ii) 8 years?
iii) 12 years?
d. Which bank is a better short-term investment? Which bank is better for those leaving money in for a longer period of time?
e. What type of sequence does the formula for Student Friendly Bank create? What type of function is the formula?
f. What type of sequence does the formula for Neighborhood Bank create? What type of function is the formula?
ALGBERA 1 HW 7-8
For questions #1-4:
a. State whether it is a growth or decay. b. State the initial value. c. State the rate of growth or decay. 1. c(t) = 100(.75)t 2. p(n) = 40(1.80)n
3. t(x) = 10,000(1.02)x 4. f(n) = 50(.1)n
5. A huge ping-pong tournament is held in Beijing, with 65,536 participants at the start of the tournament. Each round of the tournament eliminates half the participants.
a. If 𝑝(𝑟) represents the number of participants remaining after 𝑟 rounds of play, write a
formula to model the number of participants remaining.
b. Use your model to determine how many participants remain after 10 rounds of play.
c. How many rounds of play will it take to determine the champion ping-pong player?
6. Kathy plans to purchase a car that depreciates at a rate of 9.2% per year. The initial cost of the car is $21,000. Determine the value of the car after 3 years. 7. A construction company purchased some equipment costing $300,000. The value of the equipment depreciates at a rate of 14% per year.
a. Write a formula C(t) that models the value of the equipment.
b. What is the value of the equipment (to the nearest dollar) after: i) 2 years?
ii) 4 years?
iii) 6 years?
iv) 8 years?
v) 10 years?
c. Graph the points from part b on the grid below (including t = 0).
t C(t)
0 2 4 6 8 10
What type of function does the graph show?
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