notes 6-7

SECTION 6-7 LINEARIZING DATA TO FIND MODELS

WARM-UP

SKETCH A GRAPH IN THE FIRST QUADRANT FOR EACH OF THE FOLLOWING.

a. y = 3x

b. y = log x

WARM-UP

SKETCH A GRAPH IN THE FIRST QUADRANT FOR EACH OF THE FOLLOWING.

a. y = 3x

b. y = log x

WARM-UP

SKETCH A GRAPH IN THE FIRST QUADRANT FOR EACH OF THE FOLLOWING.

a. y = 3x

b. y = log x

BLOG QUESTION

BLOG QUESTION

WHAT DOES IT MEAN TO LINEARIZE DATA? DISCUSS THIS IDEA WITH A PARTNER, THEN RECORD YOUR

THOUGHTS IN YOUR BLOG. CHECK BACK TOMORROW TO SEE WHAT YOUR CLASSMATES

SAID.

EXAMPLE 1

REWRITE AS A LINEAR MODEL OF log G IN TERMS OF X.

EXAMPLE 1

REWRITE AS A LINEAR MODEL OF log G IN TERMS OF X.

G = 36(7)x

EXAMPLE 1

REWRITE AS A LINEAR MODEL OF log G IN TERMS OF X.

G = 36(7)x

logG = log(36i7 x )

EXAMPLE 1

REWRITE AS A LINEAR MODEL OF log G IN TERMS OF X.

G = 36(7)x

logG = log(36i7 x )

logG = log36 + log 7 x

EXAMPLE 1

REWRITE AS A LINEAR MODEL OF log G IN TERMS OF X.

G = 36(7)x

logG = log(36i7 x )

logG = log36 + log 7 x

logG = log36 + x log 7

EXAMPLE 2

SOLVE FOR R.

lnR = 9x − 5.52

EXAMPLE 2

SOLVE FOR R.

lnR = 9x − 5.52

R = e 9 x−5.52

EXAMPLE 2

SOLVE FOR R.

lnR = 9x − 5.52

R = e 9 x−5.52

R = e 9 xie−5.52

EXAMPLE 2

SOLVE FOR R.

lnR = 9x − 5.52

R = e 9 x−5.52

R = e 9 x

e5.52

R = e 9 xie−5.52

EXAMPLE 2

SOLVE FOR R.

lnR = 9x − 5.52

R = e 9 x−5.52

R = e 9 x

e5.52

R ≈ .004e 9 x

R = e 9 xie−5.52

EXAMPLE 3

REFER BACK TO EXAMPLE 2 IN THE BOOK. ESTIMATE THE AMOUNT OF PRACTICE TIME NEEDED

TO EXCEED 98%.

EXAMPLE 3

REFER BACK TO EXAMPLE 2 IN THE BOOK. ESTIMATE THE AMOUNT OF PRACTICE TIME NEEDED

TO EXCEED 98%.

P ≈ 15.7 lnt + 30.1

EXAMPLE 3

REFER BACK TO EXAMPLE 2 IN THE BOOK. ESTIMATE THE AMOUNT OF PRACTICE TIME NEEDED

TO EXCEED 98%.

P ≈ 15.7 lnt + 30.1

98 ≈ 15.7 lnt + 30.1

EXAMPLE 3

REFER BACK TO EXAMPLE 2 IN THE BOOK. ESTIMATE THE AMOUNT OF PRACTICE TIME NEEDED

TO EXCEED 98%.

P ≈ 15.7 lnt + 30.1

98 ≈ 15.7 lnt + 30.1-30.1-30.1

EXAMPLE 3

REFER BACK TO EXAMPLE 2 IN THE BOOK. ESTIMATE THE AMOUNT OF PRACTICE TIME NEEDED

TO EXCEED 98%.

P ≈ 15.7 lnt + 30.1

98 ≈ 15.7 lnt + 30.1-30.1-30.1

67.9 ≈ 15.7 lnt

EXAMPLE 3

REFER BACK TO EXAMPLE 2 IN THE BOOK. ESTIMATE THE AMOUNT OF PRACTICE TIME NEEDED

TO EXCEED 98%.

P ≈ 15.7 lnt + 30.1

98 ≈ 15.7 lnt + 30.1-30.1-30.1

67.9 ≈ 15.7 lnt15.715.7

EXAMPLE 3

REFER BACK TO EXAMPLE 2 IN THE BOOK. ESTIMATE THE AMOUNT OF PRACTICE TIME NEEDED

TO EXCEED 98%.

P ≈ 15.7 lnt + 30.1

98 ≈ 15.7 lnt + 30.1-30.1-30.1

67.9 ≈ 15.7 lnt15.715.7

67.9

15.7≈ lnt

EXAMPLE 3

REFER BACK TO EXAMPLE 2 IN THE BOOK. ESTIMATE THE AMOUNT OF PRACTICE TIME NEEDED

TO EXCEED 98%.

P ≈ 15.7 lnt + 30.1

98 ≈ 15.7 lnt + 30.1-30.1-30.1

67.9 ≈ 15.7 lnt15.715.7

67.9

15.7≈ lnt

t ≈ e67.9

15.7

EXAMPLE 3

REFER BACK TO EXAMPLE 2 IN THE BOOK. ESTIMATE THE AMOUNT OF PRACTICE TIME NEEDED

TO EXCEED 98%.

P ≈ 15.7 lnt + 30.1

98 ≈ 15.7 lnt + 30.1-30.1-30.1

67.9 ≈ 15.7 lnt15.715.7

67.9

15.7≈ lnt

t ≈ e67.9

15.7

≈ 75.55

EXAMPLE 3

REFER BACK TO EXAMPLE 2 IN THE BOOK. ESTIMATE THE AMOUNT OF PRACTICE TIME NEEDED

TO EXCEED 98%.

P ≈ 15.7 lnt + 30.1

98 ≈ 15.7 lnt + 30.1-30.1-30.1

67.9 ≈ 15.7 lnt15.715.7

67.9

15.7≈ lnt

t ≈ e67.9

15.7

≈ 75.55 SECONDS

EXAMPLE 4

THE MANAGER OF A TOY COMPANY ANALYZES THE PRODUCTION COSTS FOR THE COMPANY’S NEWEST

STUFFED ANIMAL. IN THE TABLE BELOW ARE COSTS C OF PRODUCING A GIVEN NUMBER OF UNITS U OF

THE TOY.

Units u 250 500 750 1000 1250

Production Cost C $68 $103 $150 $212 $314

USING YOUR GRAPHING CALCULATOR, DETERMINE WHETHER THIS DATA PRESENTED IS A LINEAR,

EXPONENTIAL, POWER, OR LOGARITHM REGRESSION. RECORD YOUR EQUATION. THEN,

ESTIMATE TO THE NEAREST DOLLAR HOW MUCH IT SHOULD COST TO PRODUCE 1100 UNITS OF THE TOY.

USING YOUR GRAPHING CALCULATOR, DETERMINE WHETHER THIS DATA PRESENTED IS A LINEAR,

EXPONENTIAL, POWER, OR LOGARITHM REGRESSION. RECORD YOUR EQUATION. THEN,

ESTIMATE TO THE NEAREST DOLLAR HOW MUCH IT SHOULD COST TO PRODUCE 1100 UNITS OF THE TOY.

USING YOUR GRAPHING CALCULATOR, DETERMINE WHETHER THIS DATA PRESENTED IS A LINEAR,

EXPONENTIAL, POWER, OR LOGARITHM REGRESSION. RECORD YOUR EQUATION. THEN,

ESTIMATE TO THE NEAREST DOLLAR HOW MUCH IT SHOULD COST TO PRODUCE 1100 UNITS OF THE TOY.

USING YOUR GRAPHING CALCULATOR, DETERMINE WHETHER THIS DATA PRESENTED IS A LINEAR,

EXPONENTIAL, POWER, OR LOGARITHM REGRESSION. RECORD YOUR EQUATION. THEN,

ESTIMATE TO THE NEAREST DOLLAR HOW MUCH IT SHOULD COST TO PRODUCE 1100 UNITS OF THE TOY.

USING YOUR GRAPHING CALCULATOR, DETERMINE WHETHER THIS DATA PRESENTED IS A LINEAR,

EXPONENTIAL, POWER, OR LOGARITHM REGRESSION. RECORD YOUR EQUATION. THEN,

ESTIMATE TO THE NEAREST DOLLAR HOW MUCH IT SHOULD COST TO PRODUCE 1100 UNITS OF THE TOY.

USING YOUR GRAPHING CALCULATOR, DETERMINE WHETHER THIS DATA PRESENTED IS A LINEAR,

EXPONENTIAL, POWER, OR LOGARITHM REGRESSION. RECORD YOUR EQUATION. THEN,

ESTIMATE TO THE NEAREST DOLLAR HOW MUCH IT SHOULD COST TO PRODUCE 1100 UNITS OF THE TOY.

USING YOUR GRAPHING CALCULATOR, DETERMINE WHETHER THIS DATA PRESENTED IS A LINEAR,

EXPONENTIAL, POWER, OR LOGARITHM REGRESSION. RECORD YOUR EQUATION. THEN,

ESTIMATE TO THE NEAREST DOLLAR HOW MUCH IT SHOULD COST TO PRODUCE 1100 UNITS OF THE TOY.

C ≈ 47.45025482(1.001513796)u

C ≈ 47.45025482(1.001513796)u

C ≈ 47.45025482(1.001513796)1100

C ≈ 47.45025482(1.001513796)u

C ≈ 47.45025482(1.001513796)1100

C ≈ 47.45025482(1.001513796)u

C ≈ 47.45025482(1.001513796)1100

C ≈ $251

HOMEWORK

HOMEWORK

P. 413 #1-16