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