patterns comparing functions geometric sequence s 100 200 300 400 500 100 300 400 500 100 200 300...

Patterns Comparing

Functions

Geometric Sequences10

0200300400

500

100

300400

500

100200300400

500

100200300400

500

100200300400

500

Arithmetic Sequence

s

Deciphering

Descriptions

200

Final Jeopardy

100 Category 1100 Category 1

Answer

3, 6, 9, ___, ___,___

Answer 100 Category 1Answer 100 Category 1

3, 6, 9, 12, 15, 18

200 Category 1200 Category 1

Answer

The first term of a sequence is 5, and the recursive rule is

an = an -1 – 6

What is the fourth term of the sequence?

Answer 200 Category 1Answer 200 Category 1

5, -1, -7, -13

The fourth term is -13.

300 Category 1300 Category 1

Answer

The first term of a sequence is 7, and the recursive rule is

an = 6an -1

What is the fourth term of the sequence?

Answer 300 Category 1Answer 300 Category 1

7, 42, 252, 1512

The fourth term is 1512.

400 Category 1400 Category 1

Answer

The first term of a sequence is 5, and the recursive rule is

an = 2an -1 + 2

What is the fourth term of the sequence?

Answer 400 Category 1Answer 400 Category 1

5, 12, 26, 545, 12, 26, 54

500 Category 1500 Category 1

Answer

The first term of a sequence is 5, and the recursive rule is

an = 3an -1 – 4

What is the fifth term of the sequence?

Answer 500 Category 1Answer 500 Category 1

5, 11, 29, 83, 2455, 11, 29, 83, 245The fifth term is The fifth term is

245.245.

100 Category 2100 Category 2

Answer

Write the recursive Write the recursive rule if rule if

aa11= 10 d = 3= 10 d = 3

Answer 100 Category 2Answer 100 Category 2Write the recursive Write the recursive

rule if rule if aa11= 10 d = 3= 10 d = 3aann = a = an-1n-1 + 3 + 3

200 Category 2200 Category 2

Answer

Write the Write the explicit/closed rule explicit/closed rule

ififaa11= 15 d = -2= 15 d = -2

Answer 200 Category 2Answer 200 Category 2

Write the rule ifWrite the rule ifaa11= 15 d = -2= 15 d = -2

aann = 15 – 2(n-1) = 15 – 2(n-1)aann = -2n + 17 = -2n + 17

300 Category 2300 Category 2

Answer

Write the first 5 Write the first 5 terms for aterms for ann=6+5n=6+5n

Answer 300 Category 2Answer 300 Category 2

Write the first 5 Write the first 5 terms for aterms for ann=6+5n=6+5n11, 16, 21, 26, 3111, 16, 21, 26, 31

400 Category 2400 Category 2

Answer

Find aFind a2020 for for 10, 6, 2, -2... 10, 6, 2, -2...

Answer 400 Category 2Answer 400 Category 2Find aFind a2020 for for 10, 6, 2, -2… 10, 6, 2, -2…aann =14 - 4n =14 - 4n

so aso a20 = 14 - 4(20) = -6620 = 14 - 4(20) = -66

500 Category 2500 Category 2

Answer

Find the closed and Find the closed and recursive rules for recursive rules for 7, 11, 15, 19, … 7, 11, 15, 19, …

Answer 500 Category 2Answer 500 Category 2

aa11 = 7 d = 4 = 7 d = 4 RecursiveRecursive: a: ann = a = an-1n-1 + 4 + 4

ClosedClosed: : aann = 7 + 4(n – = 7 + 4(n – 1) 1)

100 Category 3100 Category 3

Answer

Which function has a greater Which function has a greater rate of change between rate of change between

[2,4]?[2,4]?Function M Function O 𝒂𝒏 = 𝟏𝟓𝒏+ 𝟑𝟎 Bag Number of Skittles

1 30

2 60

3 90

4 120

Answer 100 Category 3Answer 100 Category 3

Function m: Function m: ROC=slope=25ROC=slope=25

Function oFunction o::(120 – 60)/(4 – 2) =30(120 – 60)/(4 – 2) =30

Function O has a greater rate of change.Function O has a greater rate of change.

200 Category 3200 Category 3

Answer

Which function has a greater Which function has a greater y-intercept?y-intercept?

Function R Function S 𝒂𝒏 = 𝟔𝒏−𝟑 𝒂𝒏 = 𝟑(𝟏𝟒)𝒏

Answer 200 Category 3Answer 200 Category 3

Which function has a greater y-Which function has a greater y-intercept?intercept?

Function R Function S 𝒂𝟎 = 𝟔(𝟎) −𝟑 𝒂𝟎 = −𝟑

𝒂𝟎 = 𝟑(𝟏𝟒)𝟎 𝒂𝟎 = 𝟑

Function S has a greater y-intercept.

300 Category 3300 Category 3

Answer

Which function has a smaller Which function has a smaller y-intercept?y-intercept?

Function H Function K

Month(s) Decaying Grams of Bone Matter

1 100

2 50

3 25

Month(s) Decaying Grams of Bone Matter

2 150

3 50

4 16.7

Answer 300 Category 3Answer 300 Category 3

Which function has a smaller y-Which function has a smaller y-intercept?intercept?Function H Function K

Month(s) Decaying Grams of Bone Matter

1 100

2 50

3 25

Month(s) Decaying Grams of Bone Matter

2 150

3 50

4 16.7

Function H: f(0)=200 Function K: f(0) = 1350

Function H will have a smaller y-intercept.

400 Category 3400 Category 3

Answer

Which function has a greater rate of change

between [1,3]?Function A Function B

Year Portfolio Balance

0 $5

1 $20

2 $80

3 $320

Ava earns 30% interest every year on the money she put into a retirement fund. She originally

invested $300.

Answer 400 Category 3Answer 400 Category 3

Which function has a greater rate of change between [1,3]?Function A Function B

Year Portfolio Balance

0 $5

1 $20

2 $80

3 $320

Ava earns 30% interest every year on the money she put into a retirement fund. She originally

invested $300.

Function A: ROC: (320 – 20)/(3 – 1) = 150

Function B: 𝑓ሺ𝑥ሻ= 300ሺ1+0.3ሻ𝑥

𝑓ሺ1ሻ= 300ሺ1+0.3ሻ1 = 390

𝑓ሺ3ሻ= 300ሺ1+0.3ሻ3 = 659.10

ROC: (659.1 – 390)/(3-1) = 134.55

Function A has a greater rate of change.

500 Category 3500 Category 3

Answer

Function A Function B

Year Portfolio Balance

1 $20

2 $40

3 $80

4 $160

Ava earns 50% interest every year on the money she put into a retirement fund. She originally

invested $20.

Which function has a smaller rate of change

between [2,4]?

Answer 500 Category 3Answer 500 Category 3

Function A Function B

Year Portfolio Balance

1 $20

2 $40

3 $80

4 $160

Ava earns 50% interest every year on the money she put into a retirement fund. She originally

invested $20.

Function A: ROC: (160– 40)/(4 – 2) = 60

Function B: 𝑓ሺ𝑥ሻ= 20ሺ1+0.5ሻ2

𝑓ሺ1ሻ= 20ሺ1+0.5ሻ2 = 45

𝑓ሺ4ሻ= 20ሺ1+0.5ሻ4 = 101.25

ROC: (101.25 –45)/(4-2) = 28.125

Function B has a smaller rate of change.

100 Category 4100 Category 4

Answer

Write the recursive rule if

r = 6 and a1 =7

Answer 100 Category 4Answer 100 Category 4

Write the rule if

r = 6 and a1 =7

an = 6an -1

200 Category 4200 Category 4

Answer

Write the closed rule for

2, 10, 50, 250...

Answer 200 Category 4Answer 200 Category 4

Write the rule for

2, 10, 50, 250…

a1=2 r = 5

an = 2(5)n-1

300 Category 4300 Category 4

Answer

Write the explicit/closed rule for

360,120, 40...

Answer 300 Category 4Answer 300 Category 4

Write the rule for

360,120, 40…

an = 360(1/3)n-1

400 Category 4400 Category 4

Answer

Write out the first 5 terms if

an = 3(2)n-1

Answer 400 Category 4Answer 400 Category 4

Write out the first 5 terms if

an = 3(2)n-1

3, 6, 12, 24, 48

500 Category 4500 Category 4

Answer

Write the explicit and recursive

rules for

6, 18, 54, 162, …

Answer 500 Category 4Answer 500 Category 4a1 = 6 r = 3

Recursive: an = 3an-1

Closed: an = 6(3)n-1

100 Category 5100 Category 5

Answer

You just graduated college and are thinking about how to pay off your loan of $50,000. After paying $10,000 to the bank, you decide to pay $400 each month. Write an equation to model this situation. What is the rate of change?

Answer 100 Category 5Answer 100 Category 5

Y=-400x+40000

ROC: -400

200 Category 5200 Category 5

Answer

You just graduated college and are thinking about how to pay off your loan of $50,000. After paying $10,000 to the bank, you decide to pay 6.5% each month. Write an equation to model this situation. What is the rate of decay?

Answer 200 Category 5Answer 200 Category 5

Y=40000(1-0.065)x

Y=40000(0.935)x

Rate of decay=0.065 or

6.5%

300 Category 5300 Category 5

Answer

You just graduated college and are thinking about how to pay off your loan of $50,000. After paying $10,000 to the bank, you decide to pay $400 each month. How much will you have left to pay on the 12th month?

Answer 300 Category 5Answer 300 Category 5

Y=-400(12)+40000

Y=35200

$35,200

400 Category 5400 Category 5

Answer

You just graduated college and are thinking about how to pay off your loan of $50,000. After paying $10,000 to the bank, you decide to pay 6.5% each month. If an equation was written to model this situation, what would the y-intercept be?

Answer 400 Category 5Answer 400 Category 5

Y=40000(1-0.065)0

Y=40000

500 Category 5500 Category 5

Answer

You just graduated college and are thinking about how to pay off your loan of $50,000. After paying $10,000 to the bank, you decide to pay 6.5% each month. Your friend also owes $50,000. After paying $10,000 to the bank, your friend decides to pay $500 each month.

Will you or your friend have a smaller average rate of change between [0,3]?

Answer 500 Category 5Answer 500 Category 5

You:f(x)=40000(1-0.065)x

f(0)=40000(1-0.065)0=40000f(3)=40000(1-0.065)3=32696.02

ROC: (32696.02-40000)/(3-0)=-

2434.66

Your Friend:f(x)=-500x + 40000ROC: -500

Double JeopardyDouble JeopardyFill in the blank

for the geometric sequence:

2, ___ , ___ , ___ ,1250

Answer

Double Jeopardy AnswerDouble Jeopardy Answer

2, , , ,1250

10,50,250

Final JeopardyFinal Jeopardy

Write all eight equations I told you to memorize for the test.

Answer

Final JeopardyFinal Jeopardy