Linearizing Data to Find Models

1. SECTION 6-7
LINEARIZING DATA TO FIND MODELS

2. WARM-UP
SKETCH A GRAPH IN THE FIRST QUADRANT FOR
EACH OF THE FOLLOWING.
a. y = 3 x
b. y = log x

3. WARM-UP
SKETCH A GRAPH IN THE FIRST QUADRANT FOR
EACH OF THE FOLLOWING.
a. y = 3 x
b. y = log x

4. WARM-UP
SKETCH A GRAPH IN THE FIRST QUADRANT FOR
EACH OF THE FOLLOWING.
a. y = 3 x
b. y = log x

5. BLOG QUESTION

6. 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.

7. EXAMPLE 1
REWRITE AS A LINEAR MODEL OF log G IN TERMS OF
X.

8. EXAMPLE 1
REWRITE AS A LINEAR MODEL OF log G IN TERMS OF
X.
G = 36( 7)x

9. EXAMPLE 1
REWRITE AS A LINEAR MODEL OF log G IN TERMS OF
X.
G = 36( 7)x
log G = log(36i7 )
x

10. EXAMPLE 1
REWRITE AS A LINEAR MODEL OF log G IN TERMS OF
X.
G = 36( 7) x
log G = log(36i7 ) x
log G = log36 + log 7 x

11. EXAMPLE 1
REWRITE AS A LINEAR MODEL OF log G IN TERMS OF
X.
G = 36( 7) x
log G = log(36i7 ) x
log G = log36 + log 7 x
log G = log36 + x log 7

12. EXAMPLE 2
SOLVE FOR R.
ln R = 9 x − 5.52

13. EXAMPLE 2
SOLVE FOR R.
ln R = 9 x − 5.52
9 x − 5.52
R =e

14. EXAMPLE 2
SOLVE FOR R.
ln R = 9 x − 5.52
9 x − 5.52
R =e
−5.52
R =e 9x
ie

15. EXAMPLE 2
SOLVE FOR R.
ln R = 9 x − 5.52
9 x − 5.52
R =e
−5.52
R =e 9x
ie
9x
R= e
e 5.52

16. EXAMPLE 2
SOLVE FOR R.
ln R = 9 x − 5.52
9 x − 5.52
R =e
−5.52
R =e 9x
ie
9x
R= e
e 5.52
R ≈ .004e 9x

17. EXAMPLE 3
REFER BACK TO EXAMPLE 2 IN THE BOOK.
ESTIMATE THE AMOUNT OF PRACTICE TIME NEEDED
TO EXCEED 98%.

18. EXAMPLE 3
REFER BACK TO EXAMPLE 2 IN THE BOOK.
ESTIMATE THE AMOUNT OF PRACTICE TIME NEEDED
TO EXCEED 98%.
P ≈ 15.7 ln t + 30.1

19. EXAMPLE 3
REFER BACK TO EXAMPLE 2 IN THE BOOK.
ESTIMATE THE AMOUNT OF PRACTICE TIME NEEDED
TO EXCEED 98%.
P ≈ 15.7 ln t + 30.1
98 ≈ 15.7 ln t + 30.1

20. EXAMPLE 3
REFER BACK TO EXAMPLE 2 IN THE BOOK.
ESTIMATE THE AMOUNT OF PRACTICE TIME NEEDED
TO EXCEED 98%.
P ≈ 15.7 ln t + 30.1
98 ≈ 15.7 ln t + 30.1
-30.1 -30.1

21. EXAMPLE 3
REFER BACK TO EXAMPLE 2 IN THE BOOK.
ESTIMATE THE AMOUNT OF PRACTICE TIME NEEDED
TO EXCEED 98%.
P ≈ 15.7 ln t + 30.1
98 ≈ 15.7 ln t + 30.1
-30.1 -30.1
67.9 ≈ 15.7 ln t

22. EXAMPLE 3
REFER BACK TO EXAMPLE 2 IN THE BOOK.
ESTIMATE THE AMOUNT OF PRACTICE TIME NEEDED
TO EXCEED 98%.
P ≈ 15.7 ln t + 30.1
98 ≈ 15.7 ln t + 30.1
-30.1 -30.1
67.9 ≈ 15.7 ln t
15.7 15.7

23. EXAMPLE 3
REFER BACK TO EXAMPLE 2 IN THE BOOK.
ESTIMATE THE AMOUNT OF PRACTICE TIME NEEDED
TO EXCEED 98%.
P ≈ 15.7 ln t + 30.1
98 ≈ 15.7 ln t + 30.1
-30.1 -30.1
67.9 ≈ 15.7 ln t
15.7 15.7
67.9
15.7
≈ ln t

24. EXAMPLE 3
REFER BACK TO EXAMPLE 2 IN THE BOOK.
ESTIMATE THE AMOUNT OF PRACTICE TIME NEEDED
TO EXCEED 98%.
P ≈ 15.7 ln t + 30.1
98 ≈ 15.7 ln t + 30.1
-30.1 -30.1
67.9 ≈ 15.7 ln t
15.7 15.7
67.9
15.7
≈ ln t
67.9
t ≈e 15.7

25. EXAMPLE 3
REFER BACK TO EXAMPLE 2 IN THE BOOK.
ESTIMATE THE AMOUNT OF PRACTICE TIME NEEDED
TO EXCEED 98%.
P ≈ 15.7 ln t + 30.1
98 ≈ 15.7 ln t + 30.1
-30.1 -30.1
67.9 ≈ 15.7 ln t
15.7 15.7
67.9
15.7
≈ ln t
67.9
t ≈e 15.7
≈ 75.55

26. EXAMPLE 3
REFER BACK TO EXAMPLE 2 IN THE BOOK.
ESTIMATE THE AMOUNT OF PRACTICE TIME NEEDED
TO EXCEED 98%.
P ≈ 15.7 ln t + 30.1
98 ≈ 15.7 ln t + 30.1
-30.1 -30.1
67.9 ≈ 15.7 ln t
15.7 15.7
67.9
15.7
≈ ln t
67.9
t ≈e 15.7
≈ 75.55 SECONDS

27. 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
$68 $103 $150 $212 $314
Cost C

28. 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.

29. 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.

30. 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.

31. 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.

32. 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.

33. 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.

34. 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.

39. C ≈ 47.45025482(1.001513796)
u

40. C ≈ 47.45025482(1.001513796) u
C ≈ 47.45025482(1.001513796)
1100

41. C ≈ 47.45025482(1.001513796) u
C ≈ 47.45025482(1.001513796)
1100

42. C ≈ 47.45025482(1.001513796) u
C ≈ 47.45025482(1.001513796)
1100
C ≈ $251

43. HOMEWORK

44. HOMEWORK
P. 413 #1-16