HW- pg. 276 (4.5) 4.1 & 4.2 Quiz TUESDAY 10-22-13 www.westex.org HS, Teacher Websites

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Nov 2, 2013 (3 years and 9 months ago)

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HW
-

pg
.
276

(
4.5
)

4.1 & 4.2 Quiz
TUESDAY 10
-
22
-
1
3

www.westex.org

HS, Teacher Websites

10
-
17
-
13

Warm up

AP Stats

The following table shows monthly premiums for a
10
-
year term life insurance policy worth
$1,000,000:

Age

Mo
nthly Premium

40

$29

45

$46

50

$68

55

$106

60

$157

65

$257

Use your calc. to turn each fraction into a decimal
rounded to the nearest hundredth.

= ____


____


____


____


____

Notice anything?








Name _________________________






Date _______

AP Stats

4 More about

Relationships

between Two Variables


4.1 Transforming to Achieve Linearity

Day 2


Objectives



Explain
how linear growth
differs from exponential growth
.



Use a logarithmic transformation to linearize a data set that can be modeled by an
exponential model.


Exponential Growth

In
linear growth
, a fixed increment is __________ to the variable in each equal time period.
_______
________ growth occurs when a variable is ____________ by a fixed number in each
equal time period. It is typical that with exponential growth the increase appears slow for a
long period and then seem to explode. Linear growth differs from exponential gr
owth in that
successive terms are related by ____________ in the linear case and _______________ in
the _______________ case.


Linear growth


increase by a fixed __________.


Exponential growth


increase by a fixed __________.


If an exponential model o
f

the form y = a∙
b
x

describes
the relationship between x and y, we can
use ______________ to _______________ the data to produce a linear relationship.


Algebraic Properties of Logarithms


l
og
b
x = y


if and only if (iff)


b
y

= x


Rules for logs:

1.

log
b

(MN
) = _________________________

2.

log
b

(M/N) = _________________________

3.

log
b

X
p

= _________________________


These properties hold for all positive values of base b except b = 1. Base 10 or base e
(2.71828…) are used most frequently.


Log
10

x = ______


log
e

x = ______






Example 4.5 Moore’s law and computer chips
-
Exponential growth

Gordon Moore, one of the founders of Intel Corporation, predicted in 1965 that the number of
transistors on an integrated circuit chip would double every 18 months. This is “Moo
re’s law,”
one way to measure the revolution in computing. Here are the data on the dates and number of
transistors for Intel microprocessors:

Processor

Date

Transistors

Processor

Date

Transistors

4004

1971

2250

486DX

1989

1,180,000

8008

1972

2,500

Pent
ium

1993

3,100,000

8080

1974

5,000

Pentium II

1997

7,500,000

8086

1978

29,000

Pentium III

1999

24,000,000

286

1982

120,000

Pentium 4

2000

42,000,000

386

1985

275,000

USE YEARS SINCE 1970 for x values

Find

LSRL. Write equation ________________________
__
__
_____________________
__

Define variables. ________________________________________________ r = ______

r
2

= ______ Interpret r
2

in context of problem. ___________________________________

_______________________________________________________________
________

Do

you think an exponential model
might describe

the relationship between years since 1970 and

# of transistors? y = ab
x

is the basic exponential growth model. We want this equation to be
_______________ so it will look linear. To transform an
exponential model we take the log of
both sides of the equation. We

will do this ONCE to see that taking

the log of both sides of

the

exponential equation linearizes the data.


y = ab
x

log y = log(ab
x
)








= __________________









= __________________

Notice that the y intercept is __________ and the slope is __________ so we have a straight
line! After this ONE time we will just remember that
when we are using an exponential model
the result is you take the log of just the _____

value
, but not the _____ value.

*For

a power model you take the
log of y &

the log of x to linearize.
*

(will see this tomorrow)


Transform the data by taking the log of y (Transi
s
tors).

Apply least
-
squares regression to the transformed data.

Find LSRL.
Write equation ___________________________________________________

Define variables. ________________________________________________ r = ______

r
2

= ______ Interpret r
2

in context of problem. ___________________________________

________________________
_______________________________________________

To do prediction
,

we need to _______ the logarithm transformation to return to the original
units of measurement.

(Take __________)




Predict transistors for Itanium 2 in 2003

______________________________
__________