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HW- pg. 276 (4.5)
4.1 & 4.2 Quiz TUESDAY 10-22-13
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
40
45
50
55
60
65
Monthly Premium
$29
$46
$68
$106
$157
$257
Use your calc. to turn each fraction into a decimal
rounded to the nearest hundredth.
46
68
106
157
257
=
____
____
____
____
____
29
46
157
68
106
Notice anything?
Name _________________________
AP Stats
4 More about Relationships between Two Variables
4.1 Transforming to Achieve Linearity Day 2
Date _______
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 growth 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 of the form y = a·bx describes the relationship between x and y, we can
use ______________ to _______________ the data to produce a linear relationship.
Algebraic Properties of Logarithms
logb x = y
Rules
1.
2.
3.
if and only if (iff)
by = x
for logs:
logb (MN) = _________________________
logb (M/N) = _________________________
logb Xp = _________________________
These properties hold for all positive values of base b except b = 1. Base 10 or base e
(2.71828…) are used most frequently.
Log10 x = ______
loge 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 “Moore’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
Pentium
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 = ______
r2 = ______ Interpret r2 in context of problem. ___________________________________
_______________________________________________________________________
Do you think an exponential model might describe the relationship between years since 1970 and
# of transistors? y = abx 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 = abx
log y = log(abx)
= __________________
= __________________
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 (Transistors).
Apply least-squares regression to the transformed data.
Find LSRL. Write equation ___________________________________________________
Define variables. ________________________________________________ r = ______
r2 = ______ Interpret r2 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 ________________________________________