1.In which year was the amount of rainfall highest? How many inches fell that year. 2.What was the...

1. In which year was the amount of rainfall highest? How many inches fell that year.

2. What was the average number of inches of rainfall in 2006?


4. During what period of years was the amount of rainfall increasing?

5. During which period was the decrease in rainfall most rapid, 1995 to 1997 or 2003 to 2006?

6. Is the graph concave up or concave down from 2001 to 2004?

7. If the actual amount of rainfall in 1990 was 48 inches, what was the average rate of change from 1990 to 1995. Please show your work

Average Rainfall in the Atlanta Area

1995 96 97 98 99 2000 01 02 03 04 05 06 07

Year

50

48

46

44

42

40

38

36

34

32

Average Rainfall

in inches

The graph at the right shows the average number of inches per

year of rainfall in the Atlanta area from 1995 to 2007.

Answer each of the following questions based on the graph.

2003, 48 in

38 in

39 in

From 1997 to 2003


1995 96 97 98 99 2000 01 02 03 04 05 06 07

Year

50

48

46

44

42

40

38

36

34

32

Average Rainfall

in inches











42 38 48 38 – – 2 3

2 3.33

2003, 48 in

38 in

39 in

From 1997 to 2003












1995 96 97 98 99 2000 01 02 03 04 05 06 07

Year

50

48

46

44

42

40

38

36

34

32

Average Rainfall

in inches

or

This section is Concave up

2003, 48 in

38 in

39 in

From 1997 to 2003












1995 96 97 98 99 2000 01 02 03 04 05 06 07

Year

50

48

46

44

42

40

38

36

34

32

Average Rainfall

in inches

or

This section is Concave down

2003, 48 in

38 in

39 in

From 1997 to 2003












1995 96 97 98 99 2000 01 02 03 04 05 06 07

Year

50

48

46

44

42

40

38

36

34

32

Average Rainfall

in inches

Down

Point of Inflection

2003, 48 in

38 in

39 in

From 1997 to 2003












1995 96 97 98 99 2000 01 02 03 04 05 06 07

Year

50

48

46

44

42

40

38

36

34

32

Average Rainfall

in inches

Down

-1.2 inches per year

1990

More about concavity

Notice that both graphs below are continually increasing.

As we move from left to right, in which graph is the rate of increase speeding up?

If a graph is concave up, its rate of increase becomes more rapid.

Notice that both graphs below are continually decreasing.

More about concavity

As we move from left to right, in which graph is the rate of decrease speeding up?

If a graph is concave down, its rate of decrease becomes more rapid.

Answers to even-numbered HW problems

S-2 4.0

S-4 1.0

S-6 1.8

S-8 Increasing from x = 0 to x = 2.4

S-10 Concave down

Ex 2 a) V(1995) = 5000

b) Concave up. It means it’s growing faster and faster as time passes.

c) The value will reach $55,000 in the year 2025.

d) The average yearly increase is approximately $15,000 per year.

e) The average yearly increase is larger from 2035 to 2045 because the graph is steeper between those years. Also, the

average yearly increase from 1995 to 2005 is only about $1,000 per year, which is less than the rate of increase in part (d).

Section 1.3

The average yearly cost of heating a house in Cobb County in 1975 was $260. Average yearly heating costs have increased $29 each year.

1. What was the average yearly cost of heating a house in Cobb County in 1992?

2. Use a formula to express the average yearly heating costs of a house in Cobb County as a function of the number of years since 1975.

Getting Formulas from Words

260 + (29)(17) = 753 The average yearly cost of heating a house in Cobb County in 1992 was $753.

H = 260 + (29)(t)

where:

H = average heating cost of house in dollars

t = number of years since 1975

Initial value Average rate of change

Some antique shops sell items on consignment. The owner of the item agrees to allow the store to sell the item for a certain initial price. If, after a period of time, the item has not sold, its price is reduced. The piece of furniture shown was originally put on sale for $1,800. After 7 months, its selling price became $1,240. If the price dropped by the same amount each month:

1. Write a formula (using functional notation) for the price P of the piece

after n months.

2, Use your formula to find out what the price will be after 1 year.

3. If you are willing to pay no more than $500 for the piece, how long will you have to wait?

P(n) = 1800 – 80n

The price will be $840 after 1 year.

If you wait 17 months, the price will be less than $500

Practice 1

The cost of installing the ceramic tile you chose for your kitchen floor is a function of both the number of tiles used and the number of hours needed to complete the job. Suppose the cost of your tile is $1.20 per tile, and the installer charges $75 per hour for labor.

1. Use a formula to express the cost of installing your ceramic tile in terms of the number of tiles, N, and the number of hours, H, the job will take.

2. Use functional notation to represent the total cost of the job if 80 tiles are needed and the job will take 8 hours. What is the total cost?

C = 1.20N + 75Hwhere C = total cost in dollars

C(80,8) = 1.20(80) + 75(8) = 696

The total cost of this job is $696.

Practice 2

Your job requires you to drive to different parts of the metro- Atlanta area. You can submit forms to be reimbursed for your travel expenses at the rate of $0.39 per mile.

Use a formula to express the amount you will be reimbursed in terms of the number of miles you drive for your job.

R = amount reimbursed in dollars

m = number of miles driven

R = .39m

Group Problem Set

The three problems on the following slide were completed in class as a graded group assignment. If you were not in class, please complete the problems on your own and turn in your work and solutions at the beginning of our next class meeting to receive full credit.

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.

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.

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.

3. 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.

Homework:

Read Section 1.4 (omit pages 92–96)

Page 97 # S-1, S-3, S-5, S-9, S-10, S-11

Pages 98–101 # 1, 4, 11, 12

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