Describing Change: Rates; Finding Average Rate Of Change - Texas Instruments TI-84 Plus Manual

TI-83, TI-83 Plus, TI-84 Plus Guide
Chapter 2
As you calculate average and other rates of change, remember that every numerical answer in
a context should be accompanied by units telling how the quantity is measured. You should
also be able to interpret each numerical answer. It is only through their interpretations that the
results of your calculations will be useful in real-world situations.

FINDING AVERAGE RATE OF CHANGE

function is just a matter of evaluating the equation at two different values of the input variable
and dividing by the difference of those input values.
We illustrate this concept using the function describing the temperature on a typical day in
May in a certain Midwestern city that is given in Example 3 of Section 2.1 of Calculus
Concepts.
The temperature referred to above is given by the function T(t)
2
− + +
=
0.8 2
t t
Press clear any functions, turn
Y= ,
function in
Y1
To find the average rate of change of the temperature between 11:30
realize that 11:30
that the average rate of change of T between 11:30
− −
(6) ( 0.5)
T T .
− −
6 ( 0.5)
Return to the home screen and type the quotient
Remember to enclose both the numerator and denominator of
the fraction in parentheses.
Finding this quotient in a single step avoids having to round
intermediate calculation results.
Recall that rate of change units are output units per input units. On average, the temperature
on a typical day in May in a certain Midwestern city decreased about 2.4
11:30 .M. and 6 P.
A
To find the average rate of change between 11:30
P. ., recall the last expression with
M
and replace 6 with 4 in two places. Press
NOTE: If you have many average rates of change to calculate, you could put the average rate
of change formula in the graphing list:
have a function in
with
80 STO
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Describing Change: Rates

o
where t is the number of hours after noon.
79 F
Plot 1
using as the input variable.
X
.M. corresponds to t = -0.5 and 6 P.
A
.
M
2ND
Y2 = ( Y1(B) – Y1(A) )/(B – A)
. Then, on the home screen, store the inputs of the two points in A and B
Y1
ALPHA A ALPHA
.
Finding an average rate of change using a
off, and enter this
. corresponds to t = 6. Then, recall
M
.M. and 6 P.
A
− −
Y1(6) Y1( 0.5)
.
− −
6 ( 0.5)
.M. and 4
A
ENTER (ENTRY)
ENTER .
( : ) 100 STO ALPHA B ENTER .
.M. and 6 P. ., first
A M
. is given by the quotient
M
o
per hour between
F
. Of course, you need to
All you need do
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