notes 6-7
DESCRIPTION
Linearizing Data to Find ModelsTRANSCRIPT
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