Unit 3 Day 2 ­ Growth and Decay Regular.notebook September 28, 2017

Have you???

[1] Taken out your packet?

[2] Grabbed a calculator?

[3] Completed the warm up?

Time left:

Warm Up

[1] 500, 400, 320...

[a] Common Ratio:

[b] Recursive Routine:

[c] 12th term:

agenda 05 MIN Warm Up

05 MIN Homework ?'s

20 MIN Lesson 3.2 Notes

15 MIN Assignment time

Unit 3 Day 2 ­ Growth and Decay Regular.notebook September 28, 2017

homework answers

homework answers

Unit 3 Day 2 ­ Growth and Decay Regular.notebook September 28, 2017

homework answers

homework answers

Unit 3 Day 2 ­ Growth and Decay Regular.notebook September 28, 2017

unıt 3: sequences

Modeling Growth & Decay

I can define orally and in writing: recursive formula, recursive rule, common difference, geometric sequence, common ratio

I can use a recursive formula to model real world situations like loans and investments. I can read and write recursive formulas with subscript notation. I can find terms of a sequence given recursively.

Learning Targets

*You will need a graphing calculator today!

Given the common ratios below, decide whether they show growth or decay. Then state the percent gain/loss.

1) 1.05

2) .84

3) 1.35

4) .93

5) 1

LT: I can use a recursive formula to model real world situations like loans and investments. LT: I can find terms of a sequence given recursively.

Unit 3 Day 2 ­ Growth and Decay Regular.notebook September 28, 2017

Growth and Decay

Growth:

Decay:

For Growth r > ____

For Decay r < ___ (but > 0)

LT: I can use a recursive formula to model real world situations like loans and investments. LT: I can find terms of a sequence given recursively.

Identify if the recursive routine represents growth or decay and state the percent change.

a) Un = (1 + 0.25)Un­1

b) Un = (1 ­ 0.3)Un­1

c) Un = (1.54)Un­1

d) Un = (.43)Un­1

growth or decay

common ratio percent change growth or decay

common ratiopercent change

growth or decay

common ratiopercent change

growth or decay

common ratio percent change

LT: I can use a recursive formula to model real world situations like loans and investments. LT: I can find terms of a sequence given recursively.

Unit 3 Day 2 ­ Growth and Decay Regular.notebook September 28, 2017

a) Identify the sequence as growth or decay.

b) Find the common ratio.

c) Give the percent change.

d) Write the recursive formula.

e) Find U20

14, 23.52, 39.5136, 66.382848, ...Ex 1)

LT: I can use a recursive formula to model real world situations like loans and investments. LT: I can find terms of a sequence given recursively.

a) Identify the sequence as growth or decay.

b) Find the common ratio.

c) Give the percent change.

d) Write the recursive formula.

Ex 2) 59, 27.73, 13.0331, 6.125557, ...

LT: I can use a recursive formula to model real world situations like loans and investments. LT: I can find terms of a sequence given recursively.

Unit 3 Day 2 ­ Growth and Decay Regular.notebook September 28, 2017

c) What is the percent change?

U1 = 14 Un = Un­1 0.3, where n > 2

Given the following example:

a) List the first four terms in the sequence

b) What is the common ratio?

d) Plot this situation on a graph.

LT: I can use a recursive formula to model real world situations like loans and investments. LT: I can find terms of a sequence given recursively.

Suppose Mr. Scardigli's Ford Focus cost $18,455.00 and loses one fifth of its value every year. a) Write a recursive formula for this situation.

b) Find its value when it is 6 years old.

c) When will its value fall less than $2000?

LT: I can use a recursive formula to model real world situations like loans and investments. LT: I can find terms of a sequence given recursively.

Unit 3 Day 2 ­ Growth and Decay Regular.notebook September 28, 2017

OYO: U1 = 12

Un = Un­1 1.25, where n > 2

a) List the first four terms in the sequence

b) What is the common ratio?

c) What is the percent change?

LT: I can use a recursive formula to model real world situations like loans and investments. LT: I can find terms of a sequence given recursively.

I can define orally and in writing: recursive formula, recursive rule, common difference, geometric sequence, common ratio

I can use a recursive formula to model real world situations like loans and investments.

I can read and write recursive formulas with subscript notation. I can find terms of a sequence given recursively.

Did you meet the goal?

Assignment:1.2 pg. 41 ­ 44

1 ­ 4, 6, 10, 16, 18­20

Quiz #1 tomorrow

Unit 3 Day 2 ­ Growth and Decay Regular.notebook September 28, 2017

Unit 3 Day 2 ­ Growth and Decay Regular.notebook September 28, 2017

1.51.03 0.92

0.4

a. growth 50% increase b. decay 60% decrease

c. growth 3% increase d. decay 9% decreaseu1 = 80

un = 1.03u n-1

u1 = 100

un = 1.5u n-1

u1 = 208

un = 0.92u n-1

u1 = 73.4375

un = 0.4u n-1

ii decay

i growth

iii constant

Unit 3 Day 2 ­ Growth and Decay Regular.notebook September 28, 2017

0.811 inches

21 bounces, 31 bounces

100 starting height, 0.2 is the percent loss

$250,000 starting amount, 2.5% annual interest

a. b. about 29 or 30 employees

year 1: 2 12 + 2 + 3 + 3 + 4 + 5 = 29

year 2: 3

year 3: 3 (or 4)

year 4: 4

year 5: 5

u0 = 2000 un = 1.085u n-1 8.5%

14 years ($6266.81)

3; I did 162/18 = 9 3 2 = 92, 6, ... 54, ... 486, ... 1458, ... 13122

118,098

248.6 million I solved the equation (1 + 0.132)x = 281.4

Unit 3 Day 2 ­ Growth and Decay Regular.notebook September 28, 2017

u10 = 117

u1 = 180

un = u n-1 - 7

u27 = -2

43.34 -681.5

0.853 8

4787

55-17