warm-up the tuition for in-state residents at georgia perimeter college in 1990 was $760 and the...
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Warm-up
The tuition for in-state residents at Georgia Perimeter College in 1990 was $760 and the tuition in 2010 was $2,140.
1.Assuming that the tuition rose by the same amount each year, write a formula to express the tuition as a function of the number of years since 1990. Make sure you explain the meaning of the letters you choose to represent the variables, and the units.
2. Use your formula to find the tuition for in-state residents at Georgia Perimeter College in 2005.
Warm-up
The tuition for in-state residents at Georgia Perimeter College in 1990 was $760 and the tuition in 2010 was $2,140.
1.Assuming that the tuition rose by the same amount each year, write a formula to express the tuition as a function of the number of years since 1990. Make sure you explain the meaning of the letters you choose to represent the variables, and the units.
2. Use your formula to find the tuition for in-state residents at Georgia Perimeter College in 2005.
M = 760 + 69t where M = tuition and t = # of years since 1990
Based on the formula, tuition in 2005 was $1,795.
1.According to Salary Schedule for public school teachers in Clayton County, Georgia, a starting teacher with no advanced degrees earns an annual salary of $36,386, while a teacher with 30 years experience and no advanced degrees earns $54,934. (http://www.clayton.k12.ga.us/administration/humanrsc/TeachSalSchd.asp)
a. Assuming that the annual salary increase is constant, use a formula to express the annual salary for a teacher with no advanced degrees in Clayton County as a function of time. Make sure you explain the meaning of the letters you choose to represent the variables, and the units.
b. Express using functional notation the annual salary of a teacher with 20 years experience, and calculate that salary.
1a. S = 36,386 + 618.27n, where S = the salary in dollars and n = the number of years experience.
Initial salary
54,934 – 36,38630
Salary increase per year
1.According to Salary Schedule for public school teachers in Clayton County, Georgia, a starting teacher with no advanced degrees earns an annual salary of $36,386, while a teacher with 30 years experience and no advanced degrees earns $54,934. (http://www.clayton.k12.ga.us/administration/humanrsc/TeachSalSchd.asp)
a. Assuming that the annual salary increase is constant, use a formula to express the annual salary for a teacher with no advanced degrees in Clayton County as a function of time. Make sure you explain the meaning of the letters you choose to represent the variables, and the units.
b. Express using functional notation the annual salary of a teacher with 20 years experience, and calculate that salary.
1a. S = 36,386 + 618.27n, where S = the salary in dollars and n = the number of years experience.
b. S(20) = 36,386 + 618.27(20) = 48,751.40. The salary of a Clayton County teacher with 20 years experience and no advanced degrees is $48,751.40.
2. Budget Rental Car has different payment plans. One plan charges $62 per day and 8 cents per mile.
a. Calculate the rental cost under this plan if you rent the car for 3 days and drive 120 miles.
b. Use a formula to express the cost of renting a car under this plan as a function of the number of days you keep it and the number of miles you drive. Identify the function and each variable you use, and state the units.
2a. The rental cost under this plan would be $195.60. b. C = 62d + .08m, where C = rental cost in dollars, d = number of days car is held, and m = number of miles driven.
3 a. The total cost of the dinner for 40 people is 290 + 22(40) = 1170. Dividing by 40 will give the amount you should charge each person in order to break even. 1170/40 = 29.25. Therefore, if you charge $29.25 per ticket you will break even.
You are selling tickets to a charity dinner you are having catered. You pay a rental fee of $290
for the chairs and tables, and you pay the caterer $22 for each person who attends the dinner.
Your goal is to break even (not to make a profit or to lose money).
a. How much should you charge per ticket if you expect 40 people to attend?
b. Use a formula to express the amount you should charge per ticket as a function of the
number of people attending. Make sure you explain the meaning of the letters you
choose to represent the variables, and the units.
c. Sales started out better than you expected. You now believe 58 people will attend the
dinner. Use the formula you developed in part (b) to express in functional notation the
amount you should charge per ticket, and then calculate that amount.
3 a. The total cost of the dinner for 40 people is 290 + 22(40) = 1170. Dividing by 40 will give the amount you should charge each person in order to break even. 1170/40 = 29.25. Therefore, if you charge $29.25 per ticket you will break even.
You are selling tickets to a charity dinner you are having catered. You pay a rental fee of $290
for the chairs and tables, and you pay the caterer $22 for each person who attends the dinner.
Your goal is to break even (not to make a profit or to lose money).
a. How much should you charge per ticket if you expect 40 people to attend?
b. Use a formula to express the amount you should charge per ticket as a function of the
number of people attending. Make sure you explain the meaning of the letters you
choose to represent the variables, and the units.
c. Sales started out better than you expected. You now believe 58 people will attend the
dinner. Use the formula you developed in part (b) to express in functional notation the
amount you should charge per ticket, and then calculate that amount.
You are selling tickets to a charity dinner you are having catered. You pay a rental fee of $290
for the chairs and tables, and you pay the caterer $22 for each person who attends the dinner.
Your goal is to break even (not to make a profit or to lose money).
a. How much should you charge per ticket if you expect 40 people to attend?
b. Use a formula to express the amount you should charge per ticket as a function of the
number of people attending. Make sure you explain the meaning of the letters you
choose to represent the variables, and the units.
c. Sales started out better than you expected. You now believe 58 people will attend the
dinner. Use the formula you developed in part (b) to express in functional notation the
amount you should charge per ticket, and then calculate that amount.
3 a. The total cost of the dinner for 40 people is 290 + 22(40) = 1170. Dividing by 40 will give the amount you should charge each person in
order to break even. 1170/40 = 29.25. Therefore, if you charge $29.25 per ticket you will break even.
b. C = where C = charge per ticket in dollars, and n = number of people attending.
c. C(58) = = 27. Therefore, if 58 people attend, you should charge $27 per ticket to break even.
58
22(58)290
n
n22290
You are selling tickets to a charity dinner you are having catered. You pay a rental fee of $290for the chairs and tables, and you pay the caterer $22 for each person who attends the dinner.
Your goal is to break even (not to make a profit or to lose money).
a. How much should you charge per ticket if you expect 40 people to attend?
b. Use a formula to express the amount you should charge per ticket as a function of the
number of people attending. Make sure you explain the meaning of the letters you
choose to represent the variables, and the units.
c. Sales started out better than you expected. You now believe 58 people will attend the
dinner. Use the formula you developed in part (b) to express in functional notation the
amount you should charge per ticket, and then calculate that amount.
3 a. The total cost of the dinner for 40 people is 290 + 22(40) = 1170. Dividing by 40 will give the amount you should charge each person in
order to break even. 1170/40 = 29.25. Therefore, if you charge $29.25 per ticket you will break even.
b. C = where C = charge per ticket in dollars, and n = number of people attending.
c. C(58) = = 27. Therefore, if 58 people attend, you should charge $27 per ticket to break even.
n
n22290
58
22(58)290
Answers to even-numbered HW problems
Ex 4 a) S = 63.2 – .4t
b) S(5) = 61.2
c) Different answers are possible
Ex 12 a) R = 25N
b) P = 10N – 9000 or P(N) = 10N – 9000
c) P(250) = – 6,500.
d) If the production level is 250 widgets per month, there is a loss of $6,500. The profit from producing 1,000 widgets is $1,000.
Section 1.4where S = swimming world record in seconds and t = the number of years since 1950
I want to fence in a rectangular garden next to a wall of my house. I have a total of 20 yards of chicken wire to use to construct the fence. I only need to construct three sides of the rectangle, since the wall of my house will serve as the fourth side. Is there a formula (function) for area of the garden in terms of the width of the garden?
x
y
Are
a
(in
squ
are
yar
ds)
Width (in yards)
64
60
56
52
48
44
40
36
32
28
24
20
16
12
8
4
1 2 3 4 5 6 7 8 9 10
The function that represents area as a function of width is
A(W) =
where A = area (in square yds) and W = width of the rectangle (in yds)
2W2W20
W A(W)
1
2
3.5
4
6
7
8.5
9.5
18
32
45.5
48
48
42
25.5
9.5
●
●
● ● ●
●
●
●
Can you guess at the maximum possible area that the garden can have?
50
x
y
Are
a
(in
squ
are
yar
ds)
Width (in yards)
64
60
56
52
48
44
40
36
32
28
24
20
16
12
8
4
1 2 3 4 5 6 7 8 9 10
●
●
● ● ●
●
●
●
50
Based on the graph, the maximum area appears to be about 50 square yards, when the width is 5 yards.
Entering equations
Viewing tables for equations
Setting table options
W A(W)
1
2
3.5
4
6
7
8.5
9.5
18
32
45.5
48
48
42
25.5
9.5
2W2W20 A(W) =
If we roll 3 standard (six-sided) dice, how likely is it that all three dice will come up sixes?
If we roll 4 dice, is it more likely or less likely that exactly 3 of the 4 will come up sixes?
If we roll N standard (six-sided) dice, the probability of getting exactly 3 sixes is given by the formula
where P represents the probability of getting exactly 3 sixes and N represents the number of dice.
N
6
5
750
)2N)(1N(N)N(P
x
P represents the probability of getting exactly 3 sixes N represents the number of dice.
N
6
5
750
)2N)(1N(N)N(P
x
1. Enter the function in the Y= menu of a graphing calculator.
P represents the probability of getting exactly 3 sixes N represents the number of dice.
N
6
5
750
)2N)(1N(N)N(P
x
1. Enter the function in the Y= menu of a graphing calculator.
2. What starting value and what increments would be most appropriate for viewing a table for this function? Explain.
P represents the probability of getting exactly 3 sixes N represents the number of dice.
N
6
5
750
)2N)(1N(N)N(P
x
1. Enter the function in the Y= menu of a graphing calculator.
2. What starting value and what increments would be most appropriate for viewing a table for this function? Explain.
3. Is there a maximum value for P? If so, what is that value? Explain what it represents.
P represents the probability of getting exactly 3 sixes N represents the number of dice.
N
6
5
750
)2N)(1N(N)N(P
x
1. Enter the function in the Y= menu of a graphing calculator.
2. What starting value and what increments would be most appropriate for viewing a table for this function? Explain.
3. Is there a maximum value for P? If so, what is that value? Explain what it represents.
4. Is there a limiting value for P? If so, what is that value?
Economists have determined that the amount of money remaining in the social security reserves, beginning in 1980 is a function of the number of years since 1980. The table shows the amount of money in the social security reserves in various years.
The amount of money is given by the formula
where D = the number of dollars in billions, and t = the number of years since 1980.
ENTER THE FUNCTION IN THE Y= MENU OF YOUR GRAPHING CALCULATOR.
94.
12511.5.4 32
t
ttD
94.
12511.5.4 32
t
ttD
Year Billions of dollars in Soc. Sec. reserves
1980 13.89
1985 20.34
1990 35.77
1995 51.08
2000 61.47
Economists have determined that the amount of money remaining in the social security reserves, beginning in 1980 is a function of the number of years since 1980. The table shows the amount of money in the social security reserves in various years.
The amount of money is given by the formula
where D = the number of dollars in billions, and t = the number of years since 1980.
ENTER THE FUNCTION IN THE Y= MENU OF YOUR GRAPHING CALCULATOR.
94.
12511.5.4 32
t
ttD
94.
12511.5.4 32
t
ttD
Year Billions of dollars in Soc. Sec. reserves
1980 13.89
1985 20.34
1990 35.77
1995 51.08
2000 61.47
Economists have determined that the amount of money remaining in the social security reserves, beginning in 1980 is a function of the number of years since 1980. The table shows the amount of money in the social security reserves in various years.
The amount of money is given by the formula
where D = the number of dollars in billions, and t = the number of years since 1980.94.
12511.5.4 32
t
ttD
1. Use functional notation to represent the amount of money in the social security reserves in 1993 and determine that amount.
2. Explain what is meant by D(0), and find its value.
3. Based on the function, in what year did the amount of money in the social security reserves reach a maximum? What was the amount?
4. Based on the function, in what year will the social security run out of money?
The following questions should be answered using the table options on your graphing calculator.
Year Billions of dollars in Soc. Sec. reserves
1980 13.89
1985 20.34
1990 35.77
1995 51.08
2000 61.47
Economists have determined that the amount of money remaining in the social security reserves, beginning in 1980 is a function of the number of years since 1980. The table shows the amount of money in the social security reserves in various years.
The amount of money is given by the formula
where D = the number of dollars in billions, and t = the number of years since 1980.94.
12511.5.4 32
t
ttD
1. Use functional notation to the represent the amount of money in the social security reserves in 1993 and determine that amount.
D(13) = 45.34 billion. The amount of money in the social security reserves in 1993 was $45.34 billion.
$ 45,340,000,000
Year Billions of dollars in Soc. Sec. reserves
1980 13.89
1985 20.34
1990 35.77
1995 51.08
2000 61.47
Economists have determined that the amount of money remaining in the social security reserves, beginning in 1980 is a function of the number of years since 1980. The table shows the amount of money in the social security reserves in various years.
The amount of money is given by the formula
where D = the number of dollars in billions, and t = the number of years since 1980.94.
12511.5.4 32
t
ttD
2. Explain what is meant by D(0), and find its value.
D(0) represents the amount of money in the social security reserves in 1980.
$ 13,889,000,000
D(0) = $ 13.889 billion
Year Billions of dollars in Soc. Sec. reserves
1980 13.89
1985 20.34
1990 35.77
1995 51.08
2000 61.47
Economists have determined that the amount of money remaining in the social security reserves, beginning in 1980 is a function of the number of years since 1980. The table shows the amount of money in the social security reserves in various years.
The amount of money is given by the formula
where D = the number of dollars in billions, and t = the number of years since 1980.94.
12511.5.4 32
t
ttD
3. Based on the function, in what year did the amount of money in the social security reserves reach a maximum? What was the amount?
Social security reserves reached a maximum in 2004. The maximum
amount was $64.32 billion.$ 64,320,000,000
Year Billions of dollars in Soc. Sec. reserves
1980 13.89
1985 20.34
1990 35.77
1995 51.08
2000 61.47
Economists have determined that the amount of money remaining in the social security reserves, beginning in 1980 is a function of the number of years since 1980. The table shows the amount of money in the social security reserves in various years.
The amount of money is given by the formula
where D = the number of dollars in billions, and t = the number of years since 1980.94.
12511.5.4 32
t
ttD
4. Based on the function, in what year will the social security run out of money?
Based on the function, social security reserves will run out by 2022.
Year Billions of dollars in Soc. Sec. reserves
1980 13.89
1985 20.34
1990 35.77
1995 51.08
2000 61.47
Homework:
Read Section 2.1 (through top half of page 117)
Page 123-124 # S-8, S-12, S-17, S-23
Pages 125-129 # 3, 6, 21