Finding A Log Function To Model Data - Texas Instruments TI-84 Plus Manual

TI-83, TI-83 Plus, TI-84 Plus Guide
We continue to use the data in Table 1.17 of the text. Our input
data is already small so we need not align to smaller values.
Return to the home screen. Following the same procedure that
you did to find a linear function, find the exponential function
and paste the equation into the
pressing
STAT ► [CALC] 0 [ExpReg] VARS
1 [Function] 1 [Y1].
Press
ENTER
paste it into the
to view . Press
Y1
to draw the scatter plot and the graph
of the function.
As the percentage differences indicate, the function gives a very
good fit for the data. To estimate the town's population seven
years after the closing of the mill, evaluate the function in
= 7.
We predict the population to be about 1817 people seven years
after the closing of the mill.
•
Do not confuse the percentage differences found from the data with the percentage change
for the exponential function. The constant percentage change in the exponential function
is (b − 1)100%. The constant percentage change for the function is a single value
y = ab
x
whereas the percentage differences calculated from the data are many different numbers.
In this section we also consider another function that can be used to fit data – the log function.
This function is the inverse function for the exponential function discussed first in this section.
We recognize when to use this function by considering the behavior of the data rather than a
numerical test involving differences.
FINDING A LOG FUNCTION TO MODEL DATA Use your calculator to find a log
equation of the form y = a + b ln x. We illustrate finding this function with the air pressure and
altitude data in Table 1.18 in Section 1.2 of Calculus Concepts.
Air pressure
(inches of mercury)
Altitude
(thousands of feet)
Clear the data that is currently in lists
altitude data in
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location of the
Y1
to find the equation and
location. Press
Y1 Y=
ZOOM 9 [ZoomStat]
13.76
L1
. (If you wish, clear list
L2
list by
Y=
► [Y−VARS]
at x
Y1
5.56 2.14
20 40 60
and . Enter the air pressure data in
L2
, but it is not necessary to do so.)
L3
0.82 0.33
80 100
and the
L1
29