ALGEBRA U6 HW 6-1 Linear Vs Exponential Functions
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ALGEBRA U6 HW 6-1 Linear vs Exponential Functions
1 1. Use the function f(x) = x 5 to fill in the table below and graph. 2
x f(x)
0 a) What type of function is this 1 and why?
2
3 b) What is the rate of change? 4
5 c) 6 What is the domain?
d) What is the range?
x 1 2. Use the function g(x) = to fill in the table below and graph. 3
x g(x)
-3 a) What type of function is this and why? -2
-1 b) What is the 0 rate of change?
1
2 c) What is the domain? 3
d) What is the range?
3. Two band mates have only 7 days to spread the word about their next performance. Walt thinks they can each (Walt AND Allie) pass out 100 fliers a day for 7 days and they will have done a good job in getting the news out. Allie has a different strategy. She tells 10 of her friends about the performance on the first day and asks each of her 10 friends to each tell a friend on the second day and then everyone who has heard about the concert to tell a friend on the third day and so on, for 7 days (assume that students make sure they are telling someone who has not already been told).
a) Fill in the tables below:
Walt Allie
(day) (people x reached) f(x)
1 10
2 100
b) What type of function is illustrated by Walt’s table? Explain.
c) What type of function is illustrated by Allie’s table? Explain.
d) Which band mate’s idea would reach more people, Walt’s or Allie’s? 4. Which of the following represents an expression?
(1) x 7 4 (3) 3x 2 5
(2) 5x 8 12 (4) 2X 2 30
ALGEBRA U6 HW 6-2 Identifying Functions
Identify the following equations as Linear, Quadratic, or Exponential. Justify your choice.
1. 2x2 3 18 ______2. 3 5x 20 ______
3. 2a 3ax 2 24 ______4. 5x 125 ______
5. 30 6x 8 ______6. 64 4x ______
7. Do the examples below require a linear or exponential growth model?
a. An alligator population starts with 200 alligators and every year, the alligator population is 9/7 of the previous year’s population.
b. The temperature increases by 2° every 30 minutes from 8:00 a.m. to 3:30 p.m. for a July day that has a temperature of 66° at 8:00 a.m.
c. Arnold does 5 sit-ups on Monday. Each day increases his set by 1 more than the previous day. By Saturday he can do 10 sit-ups.
d. In a bank account for Antwain’s college fund there is $5,000. Each year the account increases by 1.5%. 8. Which situation could be modeled by using a linear function?
(1) A bank account balance that grows at a rate of 5% per year, compounded annually (2) A population of bacteria that doubles every 4.5 hrs (3) The cost of cell phone service that charges a base amount plus 20 cents per minute (4) The concentration of medicine in a person’s body that decays by a factor of one-third very hour
9. The table below shows the balance in a savings account for different years.
Does it illustrate a linear or exponential function? Justify your answer.
Year Balance, in Dollars
0 380.00
10 562.49
20 832.63
30 1232.49
40 1824.39
50 2700.54
10. The function represents the height, ,in feet, of an object from the ground at seconds after it is dropped. A realistic domain for this function is
(1) (2) (3) (4) all real numbers
11. Which of the following points is a solution to the system of inequalities?
(1) (1,1) (3) (4, 2)
(2) (2, -2) (4) (-2, -1)
12. The perimeter of a triangle can be represented by the expression 5x2 – 10x + 8. Write a polynomial that represents the measure of the third side. x2 - x - 4
3x2 - 4x + 5
ALGEBRA U6 HW 6-3 Exponential Growth & Decay
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. 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?
______
ALGEBRA U6 HW 6-4 Exponential Growth & Decay
1. 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?
2. 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?
3. Solve the following system algebraically.
2x + 5y = 2 y = 3x – 20 4. Solve for x:
5 2 x 4 x 7 9 9
11. Given f (n) 2x3 2 x , find f (5)
ALGEBRA U6 HW 6-5 Simple & Compound Interest
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 3 years (same).
c. If the youth group needs the money quickly (in about 3 years), 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 above for the 14 years.
b. Write a formula for the interest he will earn after 𝒕 years at Yankee Bank.
c. Write a formula for the total amount he will have after 𝒕 years at Met Bank. 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?
REVIEW QUESTIONS:
6. State the rate of change (Positive or Negative) shown in each table below.
______
7. 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?
8. Which equation below represents an exponential function? (1) 4x 2 3 19 (3) 3x 7 25
(2) 5x 125 (4) 12 2x 5
9. 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
10. Which equation represents a line that is parallel to the line whose equation is 2x – 3y = 9?
2 (3) 3 y x 4 y x 4 (1) 3 2
(2) 2 (4) 3 y x 4 y x 4 (2) 3 2