Variables+and+Patterns

=Stretching and Shrinking=

HW
2.2 and 2.3 complete with follow-up ACE 3: 5, 7, 9 MR page 27

=Variables and Patterns=

Journal
Problem 5.1 Graphing on a calculator

A1. Which two equations in the set have graphs that are similar? The two equations that are similar are Set1 and Set2.

A2. In what ways are the two graphs similar? They are similar because they have the curvy lines.

A3. In what ways are the equations for the two graphs similar? Both of the equations are odd because one of them has x to the power of two and the other one has a division.

B1. Which equation in the set has a graph that is different from the graphs of the other equations? Set2 has the most different equation.

B2. In what way is the graph different from the other graphs? It has a straight line running through the y-axis perpendicularly.

B3. Set2 is different because it just has multiplications and also has y = 5.

Follow-Up 1a. If x = 2, what is y? Y is 4

1b. If x = ⅔, what is y? Y is 1⅓.

1c. If x = 3.25, what is y? Y is 6.5.

1d. Complete the following table for the equation y = 2x


 * x || 0 || 1 || 2 || 3 || 4 || 5 || 6 ||
 * y || 0 || 2 || 4 || 6 || 8 || 10 || 12 ||

Homework
Remember, we have a quiz next class, September 18, 2007!

Please type your name below to show that you are a member and you know how to click the  button and how to click the  button:

Mr. Cooper (example)

Please log into the class wiki, add your name to the "name" list (above) and the "things we'd like to see" list. please bring 3 or more suggestions for improving our Learning Environment (due sept 24)

= =

Homework
= =

Journal
Problem 4.1

Customers Income Food/Camp costs Bike Rental Van Rental Total Cost Profit 0 0 0 0 0 0 0 1 350 125 30 700 855 -505 2 700 250 60 700 1010 -310 3 1050 375 90 700 1165 -115 4 1400 500 120 700 1475 +80 5 1750 625 150 700 1475 +275 6 2100 750 180 700 1630 +470 7 2450 875 210 700 1785 + 665 8 2800 1000 240 700 1940 +86 9 3150 1125 270 700 2095 +1055 10 3500 1250 300 700 2250 +1250

Note: all values are in dollars ($)

A. (1) Bike Rental cost rule- c=30n (c=cost of bike rental, n=number of customers) (2) Food and Camp costs rule- c=125n (c=food and camp cost, n=number of customers) (3) Van Rental cost rule- c=700 since there is just one van (c=van rental cost)

B. Rule for calculating total cost- t=155n+700 (t=total cost, 155=food and camp costs +bike rental costs for 1 person, n=number of customers)

C. Rule for calculating profit- p=-505+(195n), as –$505 is the profit obtained from one customer, and the profit increases by $195 for each customer. (n=number of customers)

Follow-Up

A. I think equation b represents the total cost for the tour organizers if they use Theo’s father’s van (which he is giving free of cost) as it shows the total cost (excluding van rental) multiplied by the number of customers. B. In my view, equation a would allow us to calculate the total cost if the customers were required to get their own bikes as it shows the rule for calculating the total cost, but without the bike rental costs.

C. In my opinion, equation c (P=350n-[125n+700]) would best represent the profit gained if the customers would have to get their own bikes.

Homework
= =

> Examples (above rules can be written as):
 * in algebra, when a number is multiplied by a variable, the multiplication sign is often omitted.


 * I = 350n
 * C = //πd//

Journal

 * 4.1 Heading Home**

55 mph - speed 55 x 8 = 440 55 / 2 = 27.5 (1/2) 55 / 3 = 18.3 (1/3) 27.5 / 2 = 13.75 (1/4) 13.75 x 3 = 41.25 (3/4)
 * Notes/Info** - 310 mile trip (Williamsburg -> Philadelphia)

A.
 * Time (hours) || Distance (miles) ||
 * 0 || 0 ||
 * 1 || 55 ||
 * 2 || 110 ||
 * 3 || 165 ||
 * 4 || 230 ||
 * 5 || 285 ||
 * 6 || 340 ||
 * 7 || 395 ||
 * 8 || 450 ||

(coordinate graph- Coming soon!)

B. 1. The total distance traveled at 3 hours is 165 miles. 2. The total distance traveled at 4.5 hours is 257.5 miles (230 + 27.5). 3. The total distance traveled at 5.25 hours is 298.75 miles (285 + 13.75).

C. 1. If the students keep driving for 10 hours at a steady speed of 55 mph, they would travel 550 miles (10 x 55). 2. If they keep driving for 12 1/3 hours, they would travel 678.3 (55 x 12 = 660 + 18.3) miles. 3. If they keep driving for 15 hours, they would travel 825 (55 x 15) miles.

D. For any given time, to calculate the distance driven while going 55 miles per hour, you would have to multiply the given time by 55, the answer is the distance driven in that time.

E. t x 55=d (55t=d)


 * Follow-up**

1. To find the distance traveled after 3.25 hours, I would use the table by finding how many hours driven in 3 hours (165), plus .25 of the difference between hours 3 and 4 (230 - 165=55. 55 / 4=13.75). I would use graph by connecting the points and then estimate the amount driven. Using the equation, I would multiply 3 by 55, then add 13.75 (55 / 4).

2. a. If the students were traveling at an average of 55 miles per hour, then they would reach Richmond, which is 55 miles from Williamsburg, in one hour. b. If the students were traveling at an average of 55 miles per hour, they would reach Baltimore, which is about .75 of the way from Williamsburg to Philadelphia (310 / 4=77.5 miles), in about 1.2 or 1 2/5 hour (77.5 - 55=22.5, 55 - 22.5=32.5, 55 / 2 27.5, 55 / 3=18.3, 55 / 2.5 22, 55 / 22.5=2 2/5). c. To reach Philadelphia from Williamsburg, 310 miles, with an average speed of 55 miles per hour, it would take the riders about 5.5 hours. (310 - 285=25, 55 - 25=30, 55 / 25=2.5)


 * 4.2 Changing Speed**

A.
 * Time (hours) || Distance (miles) ||
 * 0 || 0 ||
 * 1 || 50 ||
 * 2 || 100 ||
 * 3 || 150 ||
 * 4 || 200 ||
 * 5 || 250 ||
 * 6 || 300 ||
 * 7 || 350 ||
 * 8 || 400 ||

(coordinate graph)


 * Time (hours) || Distance (miles) ||
 * 0 || 0 ||
 * 1 || 65 ||
 * 2 || 130 ||
 * 3 || 195 ||
 * 4 || 260 ||
 * 5 || 325 ||
 * 6 || 390 ||
 * 7 || 455 ||
 * 8 || 520 ||

(coordinate graph)

B. The tables for the three speeds are similar because they all compare the same variables, and increase at a steady rate. The tables are different because the data they share vary according to the average speed.

C. The graphs for the three speeds are similar since they are comparing the same variables, and only the average speed (amount the data is increasing by each data point) are different.

D. 1. For the average speed of 65 mph, which means each hour, 65 miles are covered, so that is the pattern of change in the data that helps calculate the distance for any given time. So, to find the distance traveled at any given time, you would have to multiply 65 by the number of hours that they have been traveling. 2. The symbolic equation for the above rule is 65t = d, where t stands for the time they have been traveling and d, for the total distance covered.

E. 1. When the average speed is 50 mph, the pattern of change int he data is that by the end of every hour, another 50 miles will have been covered. So, to find the distance traveled at any given time, you would have to multiply 50 by the number of hours that they have been traveling. 2. The symbolic equation for the above rule is 50t = d, where t stands for the time they have been traveling and d, for the total distance covered.

F. The rules of calculating the three speeds are similar because all three of them need the average speed multiplied by the amount of time traveled to find the total distance covered. They are different since the speeds are different, resulting in a change of data, compared to one another.


 * Follow-up**

1. The equation d = 60t means the average speed Malcolm was traveling at was 60 mph, so to find how many miles he had covered in any number of hours, you would have to multiply 60 by the amount of time.

2. To reach Philadelphia from Williamsburg, which is a 310 mile trip, at an average speed of 50 mph, it would take about 6 1/5 hours. Traveling at 65 mph, it would take 4 3/4 hours.

Homework
= = Ace 4: 1, 8, 9, 13

= =

Journal Problem 3.3 Predicting Profit
for **10** people it would cost about ~ **150$** for **25** people it would cost about ~ **380$** for **40** people it would cost about ~ **600$** So as you can see the profit from each person is about **15$**. for about~ **200$** they will need **14** people for about~ **500$** they will need **34** people for about~ **600$** they will need **40** people The profit increases by about 15$ for each person who joins the tour. On the graph it is shown by 80's because the scale is by five. So there is a pattern because it always increases by 80 so you can see it on the graph. It would change in the graph when it is increased because they have to pay less while getting more money.The graph would have bigger gaps between each point. for **1** person it would be about~ **15$** for **2** people it would be about~ **30$** for **3** people it would be about~ **45$** for **100** people it would be about~ **150$** the estimated profit for any amount of customers in this case is about~ 15$.
 * A.**
 * B.**
 * C.**
 * D.**
 * Problem 3.3 Follow Up**

Homework
Ace 3: 1, 2, 5, 6, 10 = =

= =

Journal 3.1: Renting Bicycles
Rocky's Rental Fees: Adrian's Rental Fees: Coordinate Graph:
 * Number of Bikes || 5 || 10 || 15 || 20 || 25 || 30 || 35 || 40 || 45 || 50 ||
 * Renal Fee ($) || 400 || 535 || 655 || 770 || 875 || 975 || 1070 || 1140 || 1180 || 1200 ||
 * Number of Bikes || 5 || 10 || 15 || 20 || 25 || 30 || 35 || 40 || 45 || 50 ||
 * Rental Fee ($) || 180 || 300 || 440 || 600 || 780 || 900 || 1020 || 1200 || 1380 || 1500 ||
 * 1) After looking at the tables and graphs I deduced that if the company owners decied to rent less than 37 bikes then they should use Adrian's Bike Shop because they have inexpensive fees. But if they decide to rent more thn 37 bikes then they should use Rocky's Cycle Center because they have inexpensive fees.
 * 2) A pattern I found from Rocky's graph: After connnecting the points, the line implies a pattern of increasing steadily until 35 bikes and then decreasing and levelling out.
 * 3) A pattern I found from Adrian's graph: After conecting the points, the line implies a pattern of inceasing steadily, not decreasing or levelling out.
 * 4) A pattern I found from Rocky's table: I see the same pattern mentioned in 2, except there isn't a line, but there are differences between the number.
 * 5) A pattern I found from Adrian's table: I see the same pattern mentioned in 3, except ther isn't a line, but there are differences between the number.

Homework
= =

= =

Homework
= =

= =

Homework
= =

Homework
= = = =

Homework
= =

= =

August 14, 2007
Hand out books, course summary, and journal and homework record.