Chapter 1
HAVING THE CALCULATOR ENTER EVENLY SPACED INPUT VALUES When an
input list consists of many values that are the same distance apart, there is a calculator
command that will generate the list so that you do not have to type the values in one by one.
The syntax for this sequence command is seq(formula, variable, first value, last value,
increment). When entering years that differ by 1, the formula is the same as the variable and
the increment is 1. Any letter can be used for the variable -- we choose to use
X. We
illustrate the sequence command use to enter the input for the population data in Table 1.17 in
Section 1.3 of Calculus Concepts.
Year of mandate 0 1 2 3 4 5 6
Population 7290 5978 4902 4020 3296 2703 2216
Clear any old data from lists
L1 and L2. To enter the input data,
position the cursor in the first list so that
L1 is darkened.
Generate the list of the years of the mandate beginning with 0,
ending with 6, and differing by 1 with
2ND STAT (LIST)
►
OPS 5 [seq X,T,θ,n , X,T,θ,n , 0 , 6 , 1 ) .
Press ENTER and the sequence of years is pasted into L1. You
must manually enter the output values in
L2.
1.3.1 FINDING PERCENTAGE DIFFERENCES
When the input values are evenly spaced, use
program
DIFF to compute the percentage differences in the output data. If the data are
perfectly exponential (that is, every data point falls on the exponential function), the percent-
age change (which in this case would equal the percentage differences) in the output is
constant. If the percentage differences are close to constant, this is an indication that an
exponential model may be appropriate.
Return to the home screen. Find the percentage differences in the population data with pro-
gram
DIFF. Press PRGM and then the number that is to the left of the DIFF program location.
Press ENTER and the message on the
right appears on your screen. Press
STAT 1 [EDIT] and ► ► ► to
view the percentage differences in list
L5.
The percentage differences in list L5 are close to constant, so an exponential function will
probably give a good fit to these data.
FINDING AN EXPONENTIAL FUNCTION TO MODEL DATA Use your calculator to
find an exponential equation to model the small town population data. The exponential
function we use is of the form y = ab
x
. It is very important that you align large numbers (such
as years) whenever you find an exponential model. If you don’t align to smaller values, the
calculator may return an error message or an incorrect function due to computation errors.
Copyright © Houghton Mifflin Company. All rights reserved.
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