ALGEBRA U6HW 6-1Linear vs Exponential Functions

1.Use the function f(x) = to fill in the table below and graph.

x / f(x)
0
1
2
3
4
5
6

a) What type of function is this

and why?

b) What is the rate of change?

c) What is the domain?

d) What is the range?

x / g(x)
-3
-2
-1
0
1
2
3

2.Use the function g(x) = to fill in the table below and graph.

a) What type of function is this

and why?

b) What is the rate of change?

c) What is the domain?

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)
x / (people reached) f(x)
1 / 200
2 / 400
(day)
x / (people 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)(3)

(2)(4)

ALGEBRA U6HW6-2IdentifyingTypes of Functions

Identify the following equations as Linear, Quadratic, or Exponential. Justify your choice.

1. ______2. ______

3. ______4. ______

5. ______6. ______

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?

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.

ALGEBRA U6HW 6-3Exponential 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) = 30(1.75)t2.p(n) = 4(.80)n

3.t(x) = 5()x4.f(n) = 50(1/5)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 ?(?) represents the number of participants remaining after ? 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)6 years?iii)10 years?

7.A mouse population starts with 2,000 mice and grows at a rate of 5% per year. The number of mice after t years can be modeled by the equation, . What is the rate of change between the second year and the fifth year rounded to the nearest whole number?

(1)116(3)2205

(2)348(4)2553

8.Samuel’s Car Service will charge a flat travel fee of $4.75 for anyone making a trip. They charge an additional set rate of $1.50 per mile that is traveled. Write an equation that represents the charges as a function C(m). How much would it cost if someone went on a trip that was 160 miles?

9.Sketch the graph of all the solutions to the equation where on the grid below.

Find the average rate of change between f(2) and f(5)

ALGEBRA U6HW 6-4 Exponential Application WP

1.Tabitha purchased a house in 2002 for $179,000. The house is expected to appreciate in value about 15% per year. Which equation could be used to find the house’s value, V, after t years?

(1) V = 179,000(.85)t(3) V = 179,000(.15)t

(2) V = 179,000(1.85)t(4) V = 179,000(1.15)t

2.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.

3. The population of Tanzania in 1995 was about 28.5 million, with an annual growth rate of 3%. Predict what the population will be in the year 2008.

4.Atmospheric pressure starts at 14.7 pounds per square inch at sea level, and it goes down 19% for each mile you are above sea level. What would the atmospheric pressure be to the nearest tenth at an altitude of 6.25 miles.

5.In 2006, the number of wolves in a wildlife preserve is 5,400. The average growth rate is 3%. If this growth rate continues, how many wolves will there be in 2016?

6.A satellite television company charges a one-time installation fee and a monthly

service charge. The total cost is modeled by the function. Which statement represents the meaning of each part of the function?

(1)y is the total cost, x is the number of months of service, $90 is the installation fee, and $40 is the service charge per month

(2)y is the total cost, x is the number of months of service, $40 is the installation fee, and $90 is the service charge per month

(3)x is the total cost, y is the number of months of service, $40 is the installation fee, and $90 is the service charge per month

(4) x is the total cost, y is the number of months of service, $90 is the installation fee,

and $40 is the service charge per month

7.Solve the following system algebraically:

2x + 5y = 2

y = 3x – 20

8.Solve for x:

9.Given , find

ALGEBRA U6HW 6-5Simple & 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 (within 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 ? years at Yankee Bank.

c. Write a formula for the total amount he will have after ? 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 Carlystill work in order to have enough money to buy the car?