The TI89: Basic Operations

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The TI-89 Basic Operations
Reset the calculator 2nd 6 (MEM)?F1?3(All
memory)?Enter Enter
Apps Desktop Off/On Mode?AppsDesktop?OFF Turn
off the calculator then turn it on. Press Apps a
menu of applications appears
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Create a new folder Home?F4?BNewFold Type a name
for your new folder e.g. NewFold xyz
By default you have a folder named main, to
switch from the folder xyz to the folder
main Mode?main?Press the Right arrow key?Move
to main using the Upper arrow key?Enter Enter
Delete a new folder 2nd (Var-link)? highlight
the folder xyz?Press the White Arrow Key (to
the left of CLEAR)?Enter
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Clear the Home Screen Type few things 11 Enter,
323 Enter, etc F1?8
Clear the Home Screen Assign a value for the
variable x 99 STO x (then hit
enter) Assign a value for the variable x 33
STO y (then hit enter) Now if you press x the
calculator will return 99 and if you press y the
calculator returns 33. To clear all variables
F6 (2nd F1)?1?Enter Enter
Stopping Calculation Press ON
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• Entering Data (Rest your calculator before
  starting this activity)
• APPS?Data/Matrix?New? use the lower arrow key to
  move to the box variable and enter a name for
  your data e.g. yyy?Enter Enter
• Enter a data in the table

• Home (Now you have a data set named yyy

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Plotting Data In his example we plot the data
set yyy. ?F1(that is y) Highlight Plot
1?Enter?use the lower arrow key to scroll down to
the x-box then type c1?scroll down to the y-box
and type c2?Enter enter?F2?9(zoom data)
Deleting Data Set Apps?Data/Matrix?Enter?F6?Delete
?5(clear column)
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Entering Tables First let us enter a
function. ?F1(y1)?y1x2 Deselect Plot1 by
pressing F4. ?F4(TBLSET)?change Independent to
ask instead of auto ?F5(Table) Enter Values for
x
Deleting Rows/Tables (Independent must be at
ask) ?F5(Table)?F5 (to delete
rows) ?F5(Table)?F1?8 (to delete the
entire table)
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Split Screen Mode? Split Screen?Use the lower
arrow key to make the following changes Split
Screen? Left-Right Split 1 APP? Home Split 2
App? Graph
Remark 2nd ESC (Quit) returns calculator to the
full screen mode.
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?F6?y1 x2 ?F3 (Graph the function) F1?Save
Copy As Variable yyy Enter Enter
Now delete the function Home??F6?y1
To retrieve the graph ?F6?F1?Open?yyy
To delete a graphuse Var-Link
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1.1 Functions Given by Formulas
If your job pays 7.00 per hour, then the money M
(in dollars) that you make depends on the number
of hours h that you work.
Money 7 x Hours worked
Thinking of h as a variable whose value we may
not know until the end of the week, we say M is a
function of h and we write
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Sometimes functions depend on more than one
variable.
The price g of gasoline (in dollars per gallon)
The cost C of operating a car that gets 32 miles
per gallon

The distance d that you drive (in miles)
Exercise Find a formula for C.
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Example Borrowing Money
When you borrow money to buy a car, you pay off
the loan in monthly payments, but interest is
always calculated based on the outstanding
balance.
If you borrow P dollars at a monthly interest
rate of r and wish to pay off the total amount in
t months, then your monthly payment M is
Remark r APR / 12 (Annual Percentage
Rate)/12
Example if the monthly interest rate is 0.7
that is r 0.007, then the APR 12 x 0.007
0.084 or 8.4
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Exercise
TI-89
6000 ? p 0.004 ? r 36 ? t
179.28
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1.2 Functions Given by Tables
The population N of the United states depends on
the date d. That is N N(d) is a function of d.
Question Approximate the population of the
United States in 1975
A reasonable guess for the value of N(1975) would
be
We filled the gap by averaging
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Question Approximate the population of the
United States in 1972
Note that it doesnt make sense to estimate the
population by averaging since 1972 is not halfway
between any of the data points.
From 1970 t0 1980 the population increased from
203.30 million to 226.54 million people. That is
an increase of
226.54 203.30 23.24 million people in 10 years
That is, on average, during the decade of the
1970s the population was increasing by
This is the average yearly rate of change in N
during the 70s
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Two years of growth
Population in 1972
Population in 1972
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1.3 Functions Given by Graphs
The following graph shows the value G G(d), in
American cents, of the German mark as a function
of the date d.
Explain the meaning of G(1970)
It is the value of the German mark in 1970
What was the average yearly increase in the value
of the mark from 1975 to 1980?
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Important features of a graph include places
where it is
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The graph of a function is concave up if it has
the shape of a wire whose ends are bent upward
Concave up and increasing
Concave up and decreasing
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Concavity does not determine whether a graph is
increasing or decreasing
As we move to the right the graph gets steeper
As we move to the right the graph gets less steep
increasing at an increasing rate
increasing at a decreasing rate
Both graphs are increasing but they increase in
different ways!
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Decreases at at a decreasing rate
Decreases at an increasing rate
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1.4 Functions Given by Words
Many times mathematical functions are described
verbally
Example Water that is initially contaminated with
a concentration of 9 milligrams of pollutant per
liter of water is subject to cleaning process.
The cleaning process is able to reduce the
pollutant concentration by 25 each hour. Let
C(t) denote the concentration of pollutant in the
water t hours after the purification process
begins.
What is the concentration after 1 hour?
What is the concentration after 2 hours?
What is the concentration after t hour?
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Example A person invested 2000 in a risky stock.
Unfortunately, over the next year the value of
the stock decreased by 9 each month. Let V(t)
denote the value in dollars of the investment t
months after the stock purchase was made.
Find a formula for V(t)
Calculate V(10), V(50), V(100), V(200)
What will happen to the value in the long run?
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2.1 Tables and Trends
Example A person invested 2000 in a risky stock.
Unfortunately, over the next year the value of
the stock decreased by 9 each month. Let V(t)
denote the value in dollars of the investment t
months after the stock purchase was made.
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Make a table of values showing the initial value
of the stock and its value at the end of each of
the first 5 months.
TI-89
Home
TBLSET?independent?ask?Enter
TABLE
Enter values for the independent variable x
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Example (Logistic Growth) When a group of dears
is introduced into a limited area, one expects
that it will over time grow to the largest size
that the environment can support. The growth
formula for the dear population is
dears after t years
What is the initial dear population?
Make a table showing the dear population after
5,10, 15, 20, 25 30 years.
What will happen to the dear population after
many years?
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2.2 Graphs
We have seen that the growth formula of the dear
population is
TI-89
F2?Zoom 6
Is this a reasonable viewing window? Why not?
F2?Zoom A
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Window (? F2)? xmax40, ymax200
Grap (? F3)
Trace the graph to find an approximation of the
dear population after 2 years
F3
Type 2 and then hit Enter
What is the dear population after 2 years?
Trace the graph to find the dear population after
many years.
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2.3 Solving Linear Equations
You need a rental car for 3 days
Company Alpha charges an initial fee of 28, a
daily rate of 4, and a rate of 29 cents per mile.
Let A(m) be the cost of renting a car from
company Alpha in terms of the number m of miles
you drive.
Find a formula for A(m)
Company Beta charges an initial fee of 32, a
daily rate of 6, and a rate of 14 cents per mile.
Let B(m) be the cost of renting a car from
company Beta in terms of the number m of miles
you drive.
Find a formula for B(m)
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For what number of miles driven are the costs of
renting a car from company Alpha and the cost of
renting a car from company Beta are the same?
TI-89
F2?Zoom 6
Do you see the graphs? Why not?
F2?Zoom A
Do the graphs intersect?
Window? xmax100
F2?Zoom A
Where the two line intersect? What does it mean?
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F5 Math?Intersection
Enter twice
Move the cursor before the intersection point
Enter
Move the cursor after the intersection point
Enter
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2.4 Solving Nonlinear Equations
Recall that the growth function for the dear
population is
For planning purposes, we want to know when to
expect there to be 85 deer on the reserve.
TI-89
F2?Zoom 9
F5 Math?Intersection
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2.5 Optimization
Exercise 21 page 177 F.E. Smith has studied
population growth for the water flea. Let N
denote the population size. Smith found that G,
the rate of growth per day in the population, can
be modeled by
Draw a graph of G versus N. Include values of N
up to 350.
Window?xmax355?Graph
At what population level does the greatest rate
of growth occur?
F5 Math?maximum
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Move the cursor before the turning point
Enter
Move the cursor after the turning point
Enter
Exercise 15 Page 176
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3.1 The Geometry of Lines
One way in which straight line are characterized
is that they are determined by two points.
For instance, given any two points there is a
unique line passing through these points
Vertical intercept
Horizontal intercept
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Another way to describe a straight line is to say
that it rises or falls at the same rate
everywhere on the line
If we move one unit to the right, the line rises
by 0.5 unit.
Thus the number 0.5 is the rate of change in
height with respect to horizontal distance.
0.5 is also known by the slope of the line and
denoted by m.
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In terms of the coordinates of the two points
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Example Find the slope of the line that contains
the points (1, 2) and (5, 4).
or
Example Find the slope of the line that contains
the points (2, 3) and (6, 1).
Which line has positive slope?
Is it increasing?
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Example Find the slope of the following lines.
The slope of a horizontal line is 0.
The slope of a vertical line is undefined.
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3.2 Linear Functions
A linear function is one whose rate of change, or
slope, is always the same.
Example The amount of income tax T, in dollars,
owed to the state of Oklahoma is a linear
function of the taxable in com I that is TT(I).
According to Oklahoma income tax table a resident
taxpayer with income of 15,000 owes the sate
780. If the taxable income is 15,500, then the
table shows a tax liability of 825.
Calculate the rate of change in T with respect to
I
What does it mean?
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How much does the taxpayer owe if the taxable
income is 15,350?
780 0.09 x 350 811
Tax on an income of 15,000
The rate of change
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Example Find an equation of the line that has
slope m 5 and contains the point (-1, 6)
Solution
y m x b
y 5 x b
The point (-1, 6) should satisfy the equation y
5 x b, hence
6 5(-1) b
11 b
Thus the equation of the line is y 5 x 11
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Example Find an equation of the line passing
through (-1, 2) and (-3, -4)
Whats the slope of the line?
Therefore y 3x b and we need to calculate b.
Y 3x b 2 3(-1) b 5 b
Thus the equation of the line is y 3x 5
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Example Find an equation of a line L that
contains the point (2, 7) and is parallel to the
line y 8x 99
Since L is parallel to y 8x 99, the slope of L
is also 8.
Therefore the equation of L is y 8x b
The line L contains the point (2, 7), hence
Y 8x b 7 8(2) b -9 b
Thus the equation of L is y 8x 9
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Recall that the slope-intercept form is given by
y m x b.
y m x b
Point-Slope Form If a nonvertical line has slope
m and contains the point (x1, y1), then an
equation for the line is y - y1 m(x- x1)
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y - y1 m(x- x1)
That is the form depends on a point and the
slope. For this reason we call it the Point-Slope
Form.
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Example A line has slope m 4 and contains the
point (6, -10). Find an equation of the line.
y - y1 m(x- x1)
y (-10) 4(x 6 )
Y 10 4(x 6 )
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3.3/3.4 Modeling Data with Linear Functions
Example Due to increased public awareness on the
life-threatening of cigarette smoking, smoking in
the United States has been in the decline for the
past several decades.
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Let p represent the percent of Americans who
smoke at t years since 1900.
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92
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Let us plot the data points (t, p)
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TI-89
Reset Calculator 2nd?6?F1?3?Enter
Home
APPS
Scroll down to Variable and enter a name for your
data e.g. zzzz
Data/Matrix?3
Enter twice
Enter the data
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Remark If you wish to clear a column use the
right/left arrow to put the cursor in the column
to be cleared. Then press 2nd F1 (Utilities) and
press 5
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Home
Enter twice
? F3 (Graph)? Zoom Stat
Home?APPS?Data/Matrix?Current?F5
Change the Twovar?LinReg
Enter C1 for x and C2 for y
Enter Twice
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The graph of the plotted data pairs is called a
scattergram
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Note that we can sketch a line that comes close
to the data points.
We say that t and p are approximately linearly
related. We call the linear function y m x b
a linear model.
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Example The Pacific salmon populations for
various years are listed in the following table.
Let P represent the salmon population at t years
since 1950. Describe the data by a scattergram.
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Find a linear model that describes the
relationship between t and P.
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Find the P-intercept of the model. What does the
point represent in terms of the salmon population?
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Use the model to predict when the salmon will be
extinct.
The t-intercept is (42, 0), or P 0 when t 42.
The salmon became extinct in 1992!!!!
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3.5 Systems of equations
Definition A linear system is a set of two or
more linear equations.
Example y 2x 1 y 3x 6
Definition The solution set of a system is the
set of all ordered pairs that satisfy both
equations.
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Example Solve the system y 2x 4 y x
1
The solution is the intersection point (-1, 2)
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Example (Inconsistent System) Solve the
system y 2x 2 y 2x 4
Note that the lines are parallel!!!!
We say the system is inconsistent
The solution set is empty.
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Example (Dependent System) Solve the system
y 3x 2 2y 6x 4
Note that 2y 6x 4 is the same as
(equivalent to) y 3x 2. Why?
Therefore the two equations are the same!!
The two lines intersect at infinitely many
points!!
We say the system is dependent.
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In this section we use algebraic methods to
solve systems of linear equations.
The Substitution Method
Example Solve the system y x 5 2y
9 3x
Remember that we are looking for an ordered pair
(x, y) that satisfies both equations.
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Equation 1 y x 5 Equation 2 2y 9 3x
Satisfying the first equation, means y must be x5
2y 9 3x
2(x 5) 9 3x
2x 25 9 3x
2x 10 9 3x
2x 1 3x
1 3x 2x
1 x
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Equation 1 y x 5 Equation 2 2y 9 3x
Lets find the value of y when x 1.
y x 5
y 1 5
y 6
The solution is (1, 6)
As always ? your answer.
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Example Use the substitution method to solve the
following system 2x 4y 6 x 2y
5
Let us substitute for x in terms of y
x 2y 5
2nd equation
x 2y 5
x in terms of y
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2x 4y 6 x 2y 5
Substitute 2y 5 for x in the first equation
2x 4y 6
2(2y 5) 4y 6
22y 25 4y 6
4y 10 4y 6
8y 10 6
8y 4
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x 2y 5
Substitute ½ for y
x 4
The solution is ( -4, ½ )
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The Elimination Method (or addition method)
The sum of the left sides of two equations is
equal to the sum of the right sides.

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5y
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Example Solve the following system 4x 5y
3 3x 5y 11
Add the two equations
4x 5y 3x 5y 3 11
7x 14
x 2
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Substitute 2 for x in either of the original
equations
4x 5y 3
42 5y 3
5y 3 8
5y 5
y 1
The solution is ( 2, 1)
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Example Solve the system 3x 2y 18 6x
5y 9
Multiply both sides of the first equation by -2.
-23x -2 2y -2 18 6x 5y 9
-6 x 4 y -36 6 x 5 y 9
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-6 x 4 y -36 6 x 5 y 9
Add the two equations
-6 x 4 y 6 x 5 y -36 9
9y 27
y 3
Substitute 3 for y in either of the original
equations
6x 53 9
6x 9 15
or
x 4
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Example Solve the system 3x 2y 10
..Equation 1 4x 3 y 15
..Equation 2
To eliminate y when the equations are added
33x 32y 3 10
(-2)4x (-2)3 y (-2) 15
Simplify
9x 6y 30 8x 6y 30
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9x 6y 30 8x 6y 30
Add the two equations
9x 6y 8x 6y 30 30
x 0
Substitute 0 for x in either of the original
equations
3x 2y 10 Equation 1
3(0) 2y 10 Equation 1
2y 10
or
y -5
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4.1 Exponential Growth and Decay
Recall for a linear function y m x b, as x
increase by 1 the value of y changes by m.
An exponential function N N(t) with base a is
one that changes by constant multiples of a. That
is, when t is increased by 1, N is multiplied by
a.
In general an exponential function has the form

• If a gt 1, then N shows an exponential growth with
  growth factor a.
• If a lt 1, the N shows an exponential decay with
  decay factor a.

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There are initially 3000 bacteria in a petri
dish. Suppose that an antibiotic has been
introduced into the dish so that each hour half
of the bacteria die.
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This is an exponential function with initial
value 3000 and hourly decay factor (base) of ½.
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The first census of the United States in 1790
showed a resident population of 3.93 million
people. From 1790 through 1860, the population
grew by about 3 each year. Let N(t) be the size
of the population t years after 1790.
Is N(t) an exponential function?
Whats the growth factor?
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Suppose that because of a famine a certain
population decreased a a rate of 4. Let N(t) be
the size of population at time t.
Is N(t) an exponential function?
Whats the growth factor?
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4.2 Modeling Exponential Data
Example A freezer maintains a constant
temperature of 6 degrees Fahrenheit. An ice tray
is filled with tap water and placed in the
refrigerator to make ice. The difference between
the temperature of the water and that of the
freezer was sampled each minute and recorded in
the following table.
What is the initial temperature of the water?
69 6
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Let t be the time in minutes and D(t) the
temperature difference. Is D(t) an exponential
function?
A table of successive quotients
Find an exponential model for temperature
difference
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When will the temperature of the water reach 32
degrees?
Temp. of water D(t) 6
We need to solve the equation D(t) 6 32, that
is
TI-89 Solve(69 x 0.96t 6 32, t)
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Example One important topic of forensic medicine
is the determination of time of death. Suppose at
600 P.M. a body is discovered in a basement
where the ambient temperature is maintained at 72
degrees. At the moment of death the body
temperature was 98.6 degrees, but after death the
body temperature cools, and eventually its
temperature matches the ambient air temperature.
Beginning at 600 P.Mgt the body temperature is
measured and the difference D(t) between body
temperature and ambient air temperature is
recorded every 2 hours.
What is the body temperature at 600 P.M.?
72 12.02
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A table of successive quotients
The table suggests that D(t) is an exponential
function. What is the decay factor?
Find a formula for D(t).
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Note that D(t) Body Temp. 72 or Body
Temp D(t) 72
What was the time of death?
Solve the equation D(t) 72 98.6
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4.3 Modeling Nearly Exponential Data
The following data shows the U.S. population from
1800 to 1860.
Let t be the time in years since 1800 and N the
population in millions. Make a table for N as a
function of t.
Plot the data points
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TI-89
Reset Calculator 2nd?6?F1?3?Enter
Home
APPS
Scroll down to Variable and enter a name for your
data e.g. zzzz
Data/Matrix?3
Enter twice
Enter the data
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Remark If you wish to clear a column use the
right/left arrow to put the cursor in the column
to be cleared. Then press 2nd F1 (Utilities) and
press 5
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Home
Enter twice
? F3 (Graph)? Zoom data
Do Exercise 9 Page 309
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Find an exponential model for the data
Home?APPS?Data/Matrix?Current?F5
Change the Twovar?ExpReg
Enter C1 for x and C2 for y
Enter Twice
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