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
______________________________
__________
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