Unit 1 Lesson 1.3 Days 4 and 5 ­ Long Run Value (4).notebook

1

September 15, 2015

welcome1. Take out notebook, pencil and calculator

2. Take out assignment from yesterday

3. Complete the ACT Openers.

[5] The relationship between temperature expressed in degrees Celsius (C) and degrees Fahrenheit (F) is given by the formula C = 5/9(F - 32). If the temperature is -10 degrees Celsius, what is it in degrees Fahrenheit?

[A] -50 [B] 14 [C] 23 1/3

[D] 27 4/9 [E] 46

[6] The table shows the values of the quadratic function f for several values of x. Which one of the following best represents f?

[A] f(x) = -2x2 [B] f(x) = x2 + 3

[C] f(x) = -x2 + 3 [D] f(x) = -2x2 - 3

[E] f(x) = -2x2 + 3

Warm up: 1. u0 = 12

un = (0.45)un­1

a) Growth or Decay?b) Common Ratio?c) Percent Change?

2. 100, 115, 132.25, 152.0875...a) Growth or Decay?b) Common Ratio?c) Write a recursive formula.

Unit 1 Lesson 1.3 Days 4 and 5 ­ Long Run Value (4).notebook

2

September 15, 2015

agenda 05 MIN  Warm Up

05 MIN  Homework ?'s

30 MIN  Lesson/Investigation 1.3 

5 MIN Assignment OYO

 

homework answers

Unit 1 Lesson 1.3 Days 4 and 5 ­ Long Run Value (4).notebook

3

September 15, 2015

homework answers

homework answers

Unit 1 Lesson 1.3 Days 4 and 5 ­ Long Run Value (4).notebook

4

September 15, 2015

unıt 1: sequences

a fırst look at lımıts 

I can use my calculator and/or algebra to determine what a sequence does in the long run (limit).

I can identify if a sequence is arithmetic, geometric, shifted geometric or neither.

Learning Targets

Unit 1 Lesson 1.3 Days 4 and 5 ­ Long Run Value (4).notebook

5

September 15, 2015

Where have you heard the word "Limit" before?

How fast will humans be able to run? Is there a limit?

Usain Bolt...

1.3 Important Info: (We'll do this first one as a class)

Unit 1 Lesson 1.3 Days 4 and 5 ­ Long Run Value (4).notebook

6

September 15, 2015

This sequence is called a shifted geometric.

Now do this one in your group:

Limit: the ________ _____ _______ of a sequence.

Shifted Geometric: Includes an ________ _____ in the recursive rule.

Example:

long run value

added term

U0 = 1 Un = 2Un­1 + 100

Unit 1 Lesson 1.3 Days 4 and 5 ­ Long Run Value (4).notebook

7

September 15, 2015

Let's do this one on your calculator.

U0 = 1 Un = 2Un­1 + 100

Press ModeHighlight Sequence (SEQ)

Press y =

U0 = 1 Un = 2Un­1 + 100

Enter the following information:

*nMin= starting term number*u(n)= recursive routine to get u, press 7

to get n, press

*u(nMin)= value of the first term

Unit 1 Lesson 1.3 Days 4 and 5 ­ Long Run Value (4).notebook

8

September 15, 2015

To find the 20th term (U20), on the home screen press u(20)

Try it on your own...

Did you get...

Try one more...

U1 = 25Un = .8Un­1 +10

Find U6

Let's look at the table...

Unit 1 Lesson 1.3 Days 4 and 5 ­ Long Run Value (4).notebook

9

September 15, 2015

Assignment:1.3

pg. 48R: #1­3, 5­6, 8­9, 13­15

orC: # 1ab, 2cd, 3ab, 5­9, 11­13

Did you meet the goal? I can use my calculator and/or algebra to determine what a sequence does  in the long run. (limit)

I can identify if a sequence is arithmetic, geometric, shifted geometric, or neither.

welcome1. Take out notebook, pencil and calculator

2. Take out assignment from yesterday

3. Complete the Warm up.

[7] In the functions y = f(x), if f(k) = 2, then which of the following could be a value of k?

[A] -1 [B] 0 [C] 0.5 [D] 2.5 [E] 4

[8] The number of cars parked in a lot is a function of the time of day. In the graph, a given x-value is the number of hours after 7 am. The equation of the function is given y = -100(x - 6)2 + 5000. According to this function, how many cars could one expect to find in the lot at 4 pm on a typical day?

[A] 3900 [B] 4100 [C] 4600

[D] 4900 [E] 5000

Unit 1 Lesson 1.3 Days 4 and 5 ­ Long Run Value (4).notebook

10

September 15, 2015

Warm up:

1. Find the long­run value (limit) of the sequence algebraically.u0 = 50un = un­1 (1­.4) + 20

2. The Irondale Food Shelf Pantry started the school year with 250 canned goods. If there is a 17% donation rate per week and a 75 item usage rate, what will happen to stock available in the pantry in the long run?

agenda 05 MIN  Warm Up

05 MIN  Homework ?'s

20 MIN  Lesson/Investigation 1.3 

10 Min Quiz #2

5 MIN Assignment OYO

 

Unit 1 Lesson 1.3 Days 4 and 5 ­ Long Run Value (4).notebook

11

September 15, 2015

homework answers

homework answers

Unit 1 Lesson 1.3 Days 4 and 5 ­ Long Run Value (4).notebook

12

September 15, 2015

Recall from yesterday...

U1 = 25Un = .8Un­1 +10

Can we graph this???Of course!

Unit 1 Lesson 1.3 Days 4 and 5 ­ Long Run Value (4).notebook

13

September 15, 2015

Now let's graph it...

U1 = 25Un = .8Un­1 +10

Unit 1 Lesson 1.3 Days 4 and 5 ­ Long Run Value (4).notebook

14

September 15, 2015

Your graph should look like this. Now we will use it to find U10.

Use the trace key!

Continue using the trace key and watch the "y" value on your graph. What happens?

The value shouldapproach 50

Unit 1 Lesson 1.3 Days 4 and 5 ­ Long Run Value (4).notebook

15

September 15, 2015

Assume the terms stop changing and set the value of the next term equal to the value of the previous term. Now you have an equation to solve.

Finding Long Run Value Using Algebra

Unit 1 Lesson 1.3 Days 4 and 5 ­ Long Run Value (4).notebook

16

September 15, 2015

Recursive rule

Assign the same variable to un and un­1

Subtract 0.85c from both sides

Divide both sides by 0.15

Algebraic Method to find a limit

Quiz #2

Unit 1 Lesson 1.3 Days 4 and 5 ­ Long Run Value (4).notebook

17

September 15, 2015

Assignment:WS 1.3

Did you meet the goal? I can use my calculator and/or algebra to determine what a sequence does  in the long run. (limit)

I can identify if a sequence is arithmetic, geometric, shifted geometric, or neither.