100 200 300 400 500 100 200 300 400 500 100 200 300 ExponentialsModels Logarithms Compositions and...

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100 200 300 400 500 100 200 300 400 500 100 200 300 Exponentials Models Logarithms Compositio ns and Inverses Systems 400 500 100 200 300 400 500 100 200 300 400 500 End Round Theme Final Jeopardy

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Transcript of 100 200 300 400 500 100 200 300 400 500 100 200 300 ExponentialsModels Logarithms Compositions and...

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Exponentials 100 PointsExponentials 100 PointsExponentials 100 PointsExponentials 100 Points

25 = x

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Exponentials 100 PointsExponentials 100 PointsExponentials 100 PointsExponentials 100 Points

X = 32

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Exponentials 200 PointsExponentials 200 PointsExponentials 200 PointsExponentials 200 Points

X0 = ?

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Exponentials 200 PointsExponentials 200 PointsExponentials 200 PointsExponentials 200 Points

X0 = 1

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Exponentials 300 PointsExponentials 300 PointsExponentials 300 PointsExponentials 300 Points

Who is “e” named after and what type of number

is it?

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Exponentials 300 PointsExponentials 300 PointsExponentials 300 PointsExponentials 300 Points

Euler, irrational

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Exponentials 400 PointsExponentials 400 PointsExponentials 400 PointsExponentials 400 Points

Sketch f(x) = ex, and identify its intercepts, asymptotes (if any), and domain and range.

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Exponentials 400 PointsExponentials 400 PointsExponentials 400 PointsExponentials 400 Points

Intercepts:X-int: none Y-int:

(0,1)Asymptotes: y = 0D: all real #’sR: y>0

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Exponentials 500 PointsExponentials 500 PointsExponentials 500 PointsExponentials 500 Points

Sketch a graph of the following function:

f(x) = -2f(x) = -2xx +3 +3

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Exponentials 500 PointsExponentials 500 PointsExponentials 500 PointsExponentials 500 Points

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Logarithms 100 PointsLogarithms 100 PointsLogarithms 100 PointsLogarithms 100 Points

Write the following logarithm Write the following logarithm in exponential form:in exponential form:

loglog3381 = 481 = 4

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3344 = 81 = 81

Logarithms Logarithms 100 Points 100 PointsLogarithms Logarithms 100 Points 100 Points

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Logarithms Logarithms 200 Points200 PointsLogarithms Logarithms 200 Points200 Points

Write the following Write the following exponential equation in exponential equation in

logarithmic form:logarithmic form:

8822 = 64 = 64

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Logarithms Logarithms 200 Points200 PointsLogarithms Logarithms 200 Points200 Points

log864 = 2

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Logarithms Logarithms 300 Points300 PointsLogarithms Logarithms 300 Points300 Points

Expand the following expression:

log4x2y

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log4 + 2logx + logy log4 + 2logx + logy

Logarithms Logarithms 300 Points300 PointsLogarithms Logarithms 300 Points300 Points

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Logarithms Logarithms 400 Points400 PointsLogarithms Logarithms 400 Points400 Points

Solve:Solve:

2 ln e2 ln e66 – ln e – ln e55

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Logarithms Logarithms 400 Points400 PointsLogarithms Logarithms 400 Points400 Points

7

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Logarithms Logarithms 500 Points500 PointsLogarithms Logarithms 500 Points500 Points

Condense the following Condense the following expression:expression:

4[ ln z + ln(z + 5)] – 2 ln(z – 5)4[ ln z + ln(z + 5)] – 2 ln(z – 5)

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Logarithms Logarithms 500 Points500 PointsLogarithms Logarithms 500 Points500 Points

ln ----------ln ----------zz44(z + 5)(z + 5)44

(z – 5)(z – 5)22

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oo

Compositions&Inverse 100 PointsCompositions&Inverse 100 PointsCompositions&Inverse 100 PointsCompositions&Inverse 100 Points

f(x) = 2x2 – 1 g(x) = 3x – 3

Find (g f)(x). 

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Compositions&Inverse100 PointsCompositions&Inverse100 PointsCompositions&Inverse100 PointsCompositions&Inverse100 Points

6x6x22 – 6 – 6

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Compositions&Inverse 200 PointsCompositions&Inverse 200 PointsCompositions&Inverse 200 PointsCompositions&Inverse 200 Points

f(x) = 2x2 – 1 g(x) = 3x – 3

Find (f + g)(x). 

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2x2x22 + 3x – 4 + 3x – 4

Compositions&Inverse 200 PointsCompositions&Inverse 200 PointsCompositions&Inverse 200 PointsCompositions&Inverse 200 Points

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Compositions&Inverse 300 PointsCompositions&Inverse 300 PointsCompositions&Inverse 300 PointsCompositions&Inverse 300 Points

Find the inverse of f(x) = 2x – 2 Find the inverse of f(x) = 2x – 2

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Compositions&Inverse 300 PointsCompositions&Inverse 300 PointsCompositions&Inverse 300 PointsCompositions&Inverse 300 Points

ff—1—1(x) = 0.5x + 1(x) = 0.5x + 1

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Compositions&Inverse 400 PointsCompositions&Inverse 400 PointsCompositions&Inverse 400 PointsCompositions&Inverse 400 Points

What is the inverse of f(x) = x2 – 3?

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Compositions&Inverse 400 PointsCompositions&Inverse 400 PointsCompositions&Inverse 400 PointsCompositions&Inverse 400 Points

No InverseNo Inverse

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Compositions&Inverse 500 PointsCompositions&Inverse 500 PointsCompositions&Inverse 500 PointsCompositions&Inverse 500 Points

What is the inverse of f(x) = ex – 4?

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Compositions&Inverse 500 PointsCompositions&Inverse 500 PointsCompositions&Inverse 500 PointsCompositions&Inverse 500 Points

f f -1-1(x) = ln(x+1)(x) = ln(x+1)

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ModelsModels 100 Points100 PointsModelsModels 100 Points100 Points

A total of $12,000 is invested at A total of $12,000 is invested at an annual interest rate of 9%. an annual interest rate of 9%.

Find the balance after 5 years if Find the balance after 5 years if it is compounded monthly.it is compounded monthly.

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ModelsModels 100 Points100 PointsModelsModels 100 Points100 Points

Approximately $18,788.17

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ModelsModels 200 Points200 PointsModelsModels 200 Points200 Points

On the day of a child’s birth, a deposit of $25,000 is made in a trust fund that pays

8.75% interest, compounded continuously. Determine the balance in this account on

the child’s 25th birthday.

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ModelsModels 200 Points200 PointsModelsModels 200 Points200 Points

Approximately $222,822.57

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ModelsModels 300 Points300 PointsModelsModels 300 Points300 Points

A deposit of $5000 is made in a trust fund that pays 7.5% interest, compounded continuously. It is specified that the balance will be given to the college from which the donor graduated after the

money has earned interest for 50 years. How much will the college

receive?

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ModelsModels 300 Points300 PointsModelsModels 300 Points300 Points

Approximately Approximately $212,605.41$212,605.41

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ModelsModels 400 Points400 PointsModelsModels 400 Points400 Points

The number V of computers infected by a computer virus increases according to the model V(t) = 100e4.6052t, where t is the time in hours. Find the number of computers infected after 2 hours.

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ModelsModels 400 Points400 PointsModelsModels 400 Points400 Points

1,000,059.6

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ModelsModels 500 Points500 PointsModelsModels 500 Points500 Points

An isotope has a half-life of 2,500 years. Its An isotope has a half-life of 2,500 years. Its mass after 200 years is 12 grams. What was mass after 200 years is 12 grams. What was

the initial mass?the initial mass?

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ModelsModels 500 Points500 PointsModelsModels 500 Points500 Points

Approximately 12.684 grams

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Systems Systems 100 Points 100 PointsSystems Systems 100 Points 100 Points

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SystemsSystems 100 Points 100 PointsSystemsSystems 100 Points 100 Points

(2, -4)(2, -4)

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Systems Systems 200 Points 200 PointsSystems Systems 200 Points 200 Points

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SystemsSystems 200 Points 200 PointsSystemsSystems 200 Points 200 Points

(-3, -9)(-3, -9)

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Systems Systems 300 Points 300 PointsSystems Systems 300 Points 300 Points

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Systems Systems 300 Points 300 PointsSystems Systems 300 Points 300 Points

Infinite number of solutionsInfinite number of solutions

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Systems Systems 400 Points 400 PointsSystems Systems 400 Points 400 Points

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Systems Systems 400 Points 400 PointsSystems Systems 400 Points 400 Points

(-1, 3)(-1, 3)

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Systems Systems 500 Points 500 PointsSystems Systems 500 Points 500 Points

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Systems Systems 500 Points 500 PointsSystems Systems 500 Points 500 Points

(6, -4, 1)(6, -4, 1)

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EliminationEliminationEliminationElimination

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FINAL JEOPARDYFINAL JEOPARDYFINAL JEOPARDYFINAL JEOPARDY

What is the name of the three What is the name of the three variable elimination we learned in variable elimination we learned in

class yesterday, and who is it class yesterday, and who is it named after?named after?

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FINAL JEOPARDYFINAL JEOPARDYFINAL JEOPARDYFINAL JEOPARDY

Gaussian Elimination, named after GaussGaussian Elimination, named after Gauss


$500 $500 $400 $400 $300 $300 $200 $200 $100 $100 $500 $500 $400 $400 $300 $300 $200 $200 $100 $100 $500 $500 $400 $400 $300 $300 $200 $200 $100 $100.

$500 $500 $400 $400 $300 $300 $200 $200 $100 $100 $500 $500 $400 $400 $300 $300 $200 $200 $100 $100 $500 $500 $400 $400 $300 $300 $200 $200 $100 $100.

ConceptsSoundsMixTypes 100 200 400 300 400 300 200 400 200 100 500 100.

ConceptsSoundsMixTypes 100 200 400 300 400 300 200 400 200 100 500 100.

$100 $400 $300$200 $400 400 $200$100$100$400 $200$200$500 $500$300 $200$500 $100$300$100$300 $500$300$400$400$500.

$100 $400 $300$200 $400 400 $200$100$100$400 $200$200$500 $500$300 $200$500 $100$300$100$300 $500$300$400$400$500.

100 200 300 400 100 200 300 400 100 200 300 400 100 200 300 400 Final Jeopardy! * 100 200 300 400.

100 200 300 400 100 200 300 400 100 200 300 400 100 200 300 400 Final Jeopardy! * 100 200 300 400.

100 200 400 300 400 onetwothreefour 300 200 400 200 100 500 100.

100 200 400 300 400 onetwothreefour 300 200 400 200 100 500 100.

` $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200.

` $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200.

100 200 400 300 400 GeographyCivicsEconomicsHistory 300 200 400 200 100 500 100.

100 200 400 300 400 GeographyCivicsEconomicsHistory 300 200 400 200 100 500 100.

100 200 400 300 400 ExcavationsFallsScaffoldsCranes 300 200 400 200 100 500 100.

100 200 400 300 400 ExcavationsFallsScaffoldsCranes 300 200 400 200 100 500 100.

ItalyGermanyHitlerVocabMussolini 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500.

ItalyGermanyHitlerVocabMussolini 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500.

$ 200 200 $ 300 300 $ 400 400 $ 500 500 $ 100 $ 200 200 $ 300 300 $ 400 400 $ 500 500 $ 100 100 $ 200 200 $ 300 300 $ 400 400 $ 500 500 $ 100 100 $ 200.

$ 200 200 $ 300 300 $ 400 400 $ 500 500 $ 100 $ 200 200 $ 300 300 $ 400 400 $ 500 500 $ 100 100 $ 200 200 $ 300 300 $ 400 400 $ 500 500 $ 100 100 $ 200.

$100€¦ · $100 $400 $300 $200 $400 $200 $100 $100 $400 $200 $200 $500 $500 $300 $200 $500 $100 $300 $100 $300 $500 $300 $400 $400 $500

$100€¦ · $100 $400 $300 $200 $400 $200 $100 $100 $400 $200 $200 $500 $500 $300 $200 $500 $100 $300 $100 $300 $500 $300 $400 $400 $500

100 200 400 300 400 OrangeGreenAquaBlue 300 200 400 200 100 500 100.

100 200 400 300 400 OrangeGreenAquaBlue 300 200 400 200 100 500 100.

200 300 400 500 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500 100 CampaignsConstitutionExecutiveLegislativeVariety.

200 300 400 500 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500 100 CampaignsConstitutionExecutiveLegislativeVariety.

100 200 400 300 400 1.11.21.3stats 300 200 400 200 100 500 100.

100 200 400 300 400 1.11.21.3stats 300 200 400 200 100 500 100.

JEOPARDY! Church $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200.

JEOPARDY! Church $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200.

100 200 400 300 400 VocabDisordersStudiesMisc. 300 200 400 200 100 500 100.

100 200 400 300 400 VocabDisordersStudiesMisc. 300 200 400 200 100 500 100.

100 200 400 300 400 OrangeGreenGreyBlue 300 200 400 200 100 500 100.

100 200 400 300 400 OrangeGreenGreyBlue 300 200 400 200 100 500 100.

Jeopardy $500 $400 $300 $200 $100 $500 $400 $300 $200 $100 $500 $400 $300 $200 $400 $300 $200 $100 $500 $400 $300 $200 $100 $500 $400 $300 $200 $100 Business.

Jeopardy $500 $400 $300 $200 $100 $500 $400 $300 $200 $100 $500 $400 $300 $200 $400 $300 $200 $100 $500 $400 $300 $200 $100 $500 $400 $300 $200 $100 Business.

Transformations SymmetryAsymptotesFunctionsSketching 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500 100 200 300 400.

Transformations SymmetryAsymptotesFunctionsSketching 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500 100 200 300 400.

Start 100 200 100 400 300 200 100 400 300 200 100 400 300 200 400 300 ElectricityGeology Ecosystems Scientific Thinking 100 200 300 400 Minerals 100.

Start 100 200 100 400 300 200 100 400 300 200 100 400 300 200 400 300 ElectricityGeology Ecosystems Scientific Thinking 100 200 300 400 Minerals 100.