Brief User Guide for TI-83 Plus
Financial Application

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*Page Activated: 8/20/06
Revised: 12/8/08
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**INDEX:
**

To facilitate lookup, the instructions are divided into the following categories:

I. Interest - Simple Interest, Compound Interest, Interest
Compounded Continuously, Effective Interest Rate.

II. Annuities and Mortgages -
Ordinary Annuities, Annuities Due, Sinking Funds,

III. Loans - Car Loans, Loan Amortization Table by hand,
Loan Amortization Table Semi-Automated

method, Loan Amortization Table Calculator Program,

IV. Investments – Price of a bond; Interest to Maturity of a Bond,
Present Value, Internal Rate of

return (Irr),
Modified Internal Rate of Return (mirr),

V. Linear Programming - Graphical Method, Simplex Method,

VI. Calculus Applications - Cost,
Average Cost, Marginal Cost, Average-Cost Minimization, Cost minimization,

**General:
**
* TMV Solver - Unless otherwise indicated, all calculations will be
with the TMV Solver. To access

this, press APPS, ENTER, ENTER.

* Most of these instructions will be carried out using a problem as an example. Note that some of the

problems could be solved, possibly even easier, without the Finance APP, but this sheet deals with

that APP only.

* Minus Signs - Note that some answers will have a minus sign before them. These are there because

the calculator follows the cash-flow sign convention in which cash outflows (investments for example)

are negative and inflows are positive. For many problems, you can ignore this sign. When it's

important, that will be indicated.

* Setting N, P/Y, and C/Y - As a general rule, when there are no periodic payments, such as in

interest

the number of compounding periods a year. Notice that for daily compounding, C/Y will be set at 360

for some problems. For

set for the number of payments a year, "N" will be the number of payments, and C/Y will be set for

the number of compoundings per year.

**I. Simple and Compound Interest.**

** 1. Simple Interest:
**A student had $5000 which she did
not need for 11 months. If she invested it for 11 months at 8%

annual interest, how much did she have at the end of the 11 months?

a) Enter values so that the following display is completed: N=1; I%=8*11/12; PV = 5000; PMT=0;

P/Y =1; C/Y=1; END.

b) Set the cursor on FV and press ALPHA; SOLVE. Note that SOLVE is the third function of the

ENTER key.

c) Note that if you want the interest accumulated, then just subtract $5000 from the answer

obtained in the above operation.

**2. Compound Interest:
Ex 1**: Suppose that you
invest $5000 for 6.5 years at 5.25% interest compounded quarterly,

how much money will you have at the end of the period?

P/Y =1; C/Y=4; END.

b) Set the cursor on FV and press ALPHA; SOLVE. Note that SOLVE is the third function of the

ENTER key. Your answer should be 7017.93.

c) Note that if you want the interest accumulated, then just subtract $5000 from the answer

obtained in the above operation.

**Ex 2**:
Suppose that you have $1200 and you need $1800 in 7 years, at what
interest compounded

quarterly, will you need to invest
the money to earn this amount?

a) Enter values so that the
following display is completed: N=7; I%=5.25; PV = -1200;

PMT=0;
P/Y =1; C/Y=4; END.

b) Set the cursor on I%, and
press ALPHA; SOLVE. Note that SOLVE is the third function of the

ENTER
key. Your answer should
be 5.834 rounded to 3 decimal places.

c) Note that if you want the
interest accumulated, then just subtract $5000 from the answer

obtained in the above operation.

**EX
3: Interest Compounded Continuously:
** Although the formula A=Pe

rearranging the formula to obtain time or rate. So, I will include this example of continuous compounding.

Let's take the information in Ex 2 above except that we have interest compounded continuously.

a) Enter the information exactly as in Ex 2 except that for C/Y, enter 1E9. Do that by pressing 2, 2ND

EE (the comma key), 9, ENTER. Now, continue with item b) as in Ex 2.

**3. **
Effective Interest Rate:

Suppose that a one bank tells you that it pays
3.9% compounded monthly and another tells you

that it pays 4% compounded semi-annually. Which
one is the best investment?

a) Press APPS, ENTER, Cursor to C:EFF( and press
ENTER. (Alternatively, you may press

ALPHA C.) "EFF ("
will be pasted to the screen.

b) Enter 3.9, 12) and press ENTER. Your
interest will be 3.97%.

c) Press 2nd, ENTRY (the second function of
ENTER); then edit the entry so that you have

EFF(4, 2); then press
ENTER. Your answer will be 4.04. So, this is the best investment.

II. Annuities and Mortgages:

**1. Ordinary Annuities:
**For our purposes, an
ordinary annuity will be one in which equal payments are made at equal

periods of time, the compounding period is the same as the payment period, and the payments

are made at the end of the period.

the TMV Solver must set equal to the number of payment periods.

compounded annually, how much will you have at the end of the period?

a) Enter values so that the following display is completed: N=7; I%=6; PV = 0;PMT=-20000;

P/Y =1; C/Y=1; END.

b) Set the cursor on FV and press ALPHA, SOLVE. Note that SOLVE is the third function of the

ENTER key. Your answer should be 167876.75.

2. Annuities Due:

Annuities Due have the same setup as ordinary annuities, except that BEGIN is
highlighted

instead of END.

Ex. 1: Suppose that you
pay $500 each year into an annuity due for 7 years. If the interest is

6% compounded annually, how
much will you have at the end of the year?

a) Enter values so that the following display
is completed: N=7; I%=6; PV = 0;PMT=-500;

P/Y =1; C/Y=1; **BEGIN**

b) Set the cursor on FV and
press ALPHA, SOLVE. Note that SOLVE is the third function of the

ENTER
key. Your answer should be 4196.92, rounded to 2 decimal places.

**
3. Sinking Funds:
**Sinking funds have the same
characteristics as annuities, but they are for purposes other than an

annuity. They may be to accumulate enough money to buy a car, pay off a loan, or any other

purpose. Follow the same procedure for these as for annuities.

**
4. Mortgages:
** Suppose a family buys
a home for $200000 and makes a down payment of $20000. They take

out a $180000 mortgage at 7.5% for 30 years. What is the monthly payment required to

amortize this loan?

a) Enter values so that the following display is completed: N=360; I%=7.5; PV =

180000; FV=0; PMT=0; P/Y =12; C/Y=12; END.

b) Set the cursor on PMT and press ALPHA, SOLVE. Note that SOLVE is the third function of

the ENTER key. Your answer should be 1258.59, rounded to 2 decimal places.

Addendum: To find the total interest paid on this loan, use this formula:

Total Interest = Monthly Payment*Number of Months - Original Amount of Loan.

= 1258.59*360 -180000

= $273092.4

**5. Amortization Table for a Loan:
**

calculate several loans or several lines on a table.

Therefore, I have added a little program that I wrote to save you some work. The program follows

this explanation.

**Manual Method:
** Suppose you have an 10-year loan of $80,000.00 at 8.5 percent with payments each
month.

Make an amortization table for the first three payments. You might first want to make a table

such as the following to enter your data. The calculated data has already been entered in

this table.

Payment Number |
Amount of Payment |
Principal Payment |
Interest Payment |
Principal Balance |

0 | $80,000.00 | |||

1 | $991.89 | $425.22 | $566.67 | $79574.80 |

2 | $991.89 | $428.23 | $563.65 | 79146.54 |

3 | $991.89 | $431.26 | $560.62 | 78715.285 |

1) Press APPS, ENTER, ENTER.

2) Put the following information in the display that appears:
N=10*12; I% = 8.5; PV=80000;

FV=0; P/Y=12;C/Y = 12; END.

3) Put the cursor at PMT, press ALPHA, ENTER, and the payment of 991.885
will be displayed

opposite PMT.

4) Press 2nd, QUIT, APPS, ENTER, 9, to display bal(. We will now
calculate the balance after

each of the three payments.

5) Enter values so that your display looks like this: bal(1,1
. Press ENTER and the value

indicated in the table will be displayed.

6) Press 2nd, ENTER, and the entry will be displayed again. Edit the
entry to look like this

bal(2,2 . Press ENTER and the new balance will be displayed.

7) Follow this same procedure to calculate the balance after the third
payment.

8) Now, we will calculate the Principal Payments. Press APPS, ENTER,
0 (zero), and ∑Prn( will

appear on the screen.

9) To calculate the principal for the first payment, add numbers so that
the entry looks as follows: ∑Prn(

1,1 . For the second payment, change the display to ∑Prn( 2,2 and for the third to ∑Prn( 3,3 . Of

course, press ENTER for each calculation.

10) Finally, calculate the interest payments. Press APPS, ENTER, ALPHA, A, and
the following will be

displayed: ∑Int( . Calculate the three interest amounts the using the same procedure as with the

principal
balance and interest payments.

Of course, you could have calculated all three amounts for the first payment;
then the second etc.,

but that would have been much more work.

**Using the Program: **This is a simple program that should take only a
few minutes to enter if you

have some rudimentary knowledge of how to enter programs. You can find
information on entering

programs in your TI User Manual in the programs
section on this Website. (Click on TI

Programming Keystrokes near the bottom of the navigation panel to the left.) STCC students may

call me at the Gill ASC and make an appointment to have the program electronically transferred
to

their calculators. It takes less than five minutes,
including setup. NOTE: The colons to the left on

the lines of code are automatically entered when you enter the program by hand.

:PROGRAM: LAONAMRT

:"FKIZER V:050106"

: Disp "ENTR DATA IN APPS"

:Input "1ST PMT NO. ", B

:Input "LAST PMT NO. ", E

:1→X

:ClrList L_{1}, L_{2}, L_{3}, L_{4}

:For(P,B,E

:tmv_Pmt→L_{1}(X)

:∑Int( P,P→L_{2}(X)

:∑Prn( P,P→L_{3}(X)

:bal(P,P→L_{4}(X)

:X+1→X

:End

:Stop

**Using the Program**: Here's how to use this program, assuming you
already have it entered.

1) Follow the first three steps in the manual method described above; then
press 2nd, QUIT.

2) Pres, PRGM; cursor to the program name and press ENTER.

3) The statement 1ST PMT NO. will appear. Enter the number of the first
payment you want to

calculate
data for and press ENTER.

4) LAST PMT NO. will then appear. Enter the number for the last
payment you want to calculate

and press ENTER.
Obviously, if you want only one payment, that number will be entered for

both the first and last payment number.

5) The calculator will store the amounts for Payment, Interest, Principal
Payment, and Principal

Balance in that order in lists L_{1, }L_{2}, L_{3}, and
L_{4}.

6) To access the data tables, press STAT, ENTER.

7) You will notice that the data has only five entries (Numbers plus
decimal and negative sign, if

any.). You can read the actual number stores for entry by scrolling to
that entry and reading the

entry at the bottom of the list.

**III. Loans:
**Loans, car loans for example, have the same
structure as ordinary annuities. Let's do an example

to demonstrate that.

Ex 1: Suppose that a car costs $26000, and you pay down $4000. The balance will be paid off in

36 monthly payments with a interest of 10% per year on the unpaid balance. Find the monthly

payment.

a) Enter values so that the following display is completed: N=36; I%=10; PV = 22000;PMT=0;

FV=0; P/Y =12; C/Y=12; END.

b) Set the cursor on PMT and press ALPHA, SOLVE. Note that SOLVE is the third function of

the ENTER key. Your answer should be 709.88, rounded to 2 decimal places.

**IV. Investments: **

**
1. Bonds:
Ex 1: **Suppose
that a $1000, 10-year, 8% bond is issued when the market rate is 7.5%.

Interest is paid semiannually. What can you

a) Enter values so that the following display is completed: N=20; I%=7.5; PV =0;PMT=40;

FV=1000; P/Y =2; C/Y=2; END. It's important to realize that the cost is based on the interest

to maturity.

b) Set the cursor on PV and press ALPHA, SOLVE. Note that SOLVE is the third function of

the ENTER key. Your answer should be -1034.74, rounded to 2 decimal places.

**Ex 2: **
Suppose that you have to pay $1034.74 for a $1000, 10-year, 8% bond with
interest paid

twice a year.
What is the **interest to maturity** for the bond?

a)
Enter values so that the following display is completed: N=20; I%=0; PV =1034.74;PMT=40;

FV=1000; P/Y =2;
C/Y=2; END.

b) Set the
cursor on I% and press ALPHA,
SOLVE. Note that SOLVE is the third function of

the ENTER key. Your
answer should be 7.5%.

**2.
Present value:
** The
syntax for Net Present Value (NPV) is: npv(interest rate, CFO,
CFList[CFFreq]). Now,

let's define what these mean:

Interest Rate = the rate by which to discount the cash flows over one period.

CFO = the initial cash flow at time zero.

CFOList = A list of cash flow amounts AFTER the initilal cash flow, CFO.

CFFreq = How many there are of each amount. The default is 1.

the end of each year for the next 5 years. How much would you be willing to pay for it if you

wanted 10 percent interest per year?

PERIOD | CASH FLOWS |

0 | 0 |

1 | 100 |

2 | 200 |

3 | 300 |

4 | 400 |

5 | 500 |

a) Press STAT, ENTER to go to the lists. It
there are numbers in the list you choose to use,

you can erase those numbers by highlighting the list name,
for example L_{1}, pressing CLEAR;

then ENTER. Do not use DEL.

b) Enter the numbers starting with 100 in list L_{1. }
To enter a number, just enter it and press ENTER.

c) Press 2nd, QUIT to leave the list.

d) Press APPS, ENTER, 7. "npv(" will be pasted to the home
screen.

e) Make entries so that you have the following: npv(10, 0, L_{1}.
To enter L_{1}, press 2nd L_{1}. (L_{1}

is the second function of the number 1 key.)

f) Press ENTER. Your answer should be 1065.26 rounded to two
decimal places.

NOTE 1: Instead of using the lists, you could enter the
following:

npv(10, 0, {100, 200, 300, 400, 500}). Then press ENTER. I
frankly prefer to use lists because

of the increased flexibility.

NOTE: If you have several CONSECUTIVE cash flows, you can create
a frequency table in

another list, L_{2, }for example. You will need to enter
the frequency for each of the CFO values,

even if it is 1. Your entry then would be npv(10, 0 L_{1},
L_{2} .

**Ex. 2: **Suppose that we wanted to find the future value.
Rather than using the TMV solver for

each cash flow and adding them up, just multiply the answer from
Ex. 1 by (1+.10)^5. To do

that, press 2nd, Ans, x (multiply), (1+.10)^5. Your answer should
be 1715.61.

**Ex. 3: **Suppose that you were offered the above investment
for $800. What is the NPV?

CFO is now -800. The cash outflow is negative. So, we would
enter, npv(10, -800, L_{1}. Your

answer should be 265.26 rounded to 2 decimal places.

**3. Internal Rate of Return (Irr):**

Suppose you wanted to find the Irr for the npv example above.

a) Press APPS, ENTER, 8. The term "irr(" will be displayed on the
home screen.

b) Make entries so that you have the following: irr(-800, L_{1}.Your
answer should be 19.538. This

assumes that the numbers in the table of cash flows above have
been entered in list L_{1}.

**4. Modified Internal Rate of Return
(MIrr):**

**Step 1**: First we'll find the Future Value:

a) Press STAT, ENTER to go to the lists. It there are numbers in the
list you choose to use,

you can erase those numbers by highlighting the list name,
for example L_{1}, pressing CLEAR;

then ENTER. Do not use DEL.

b) Enter the numbers starting with 100 in list L_{1. } To
enter a number, just enter it and press ENTER.

c) Press 2nd, QUIT to leave the list.

d)
Press APPS, ENTER, ENTER to display the TMV Solver.

e) Enter values in the
display as follows:: N=5; I%=0; PV =-800; PMT=0;

FV=1715.61; P/Y =1; C/Y=; END.

Now, we want to enter a calculated value into FV. To do that, place
the cursor opposite FV, press

CLEAR to clear the value there; the do the following:

f) Press APPS, ENTER, 7. "npv(" will be pasted to the home screen.

g) Make entries so that you have the following: npv(10, 0, L_{1}).
To enter L_{1}, press 2nd L_{1}. (L_{1} is the

second function of the number 1 key.)

h) Now, we want to multiply this by (1.1)^5. To do that enter
1.1^5. You should now have

the this expression: npv(10, 0, L_{1})1.1^5. When you
move the cursor away from FV you

should have 1715.61

i) Set the cursor on I% and press ALPHA, SOLVE. Note that SOLVE is
the third function of

the ENTER key. Your answer should be 16.48 rounded to two
decimal places.

**V. Linear Programming:
**

** 1. Graphical Method:
Ex 1: **Suppose that we want to maximize the objective function
with function and constraints defined

as follows:

z=2x+5y

3x+2y≤6

-x+2y≤ 4

x≥0, y≥0

a) First rewrite the inequalities in slope-intercept form:

y≤(-3/2)x +3

y≤x/2+2

b) Press Y= and enter the expressions in Y1 and Y2. If you wish, you can do the shading by moving the

cursor over to the left and pressing ENTER until you get the third-quadrant triangle for <, but I prefer to

just graph the equations.

c) Press WINDOW and set the following: Xmin=0, Xmax=5, Ymin=0, Ymax=4. Press GRAPH and the

graphs will be displayed. You can read the points (0,2) and (2,0) from the graph, but we want to find

the point of intersection.

d) To find the intersection point press 2ND, CALC, 5(Intersect), move the cursor back to about x=.7 and

press ENTER. Press ENTER, ENTER after the cursor has moved to the other curve and x=.5, y=2.25

will be displayed.

f) We now have the points (0,2), (.5, 2.25), and (2,0) that we want to plug into the objective function. You

could do this manually fairly easily, but there may be occasions when it is not done so easily by hand.

Do the calculations with the calculator as follows:

1) Press 0, STO, X (use the [x,T,0,n] button for X), ALPHA, : (the decimal button), 2, STO, ALPHA, Y,

ALPHA, :, 2, X, +, 5, ALPHA, Y. You should now have 0→X:2→Y:2X+5Y.

2) Press ENTER and 10 will be diplayed.

3) Now, press 2ND, ENTER and change the stored values of X and Y, so that you have the following:

.5→X:2.5→Y:2X+5Y. Press ENTER and 13.5 will be displayed.

3) Now, press 2ND, ENTER and change the stored values of X and Y, so that you have the following:

2→X:0→Y:2X+5Y. Press ENTER and 4 will be displayed.

So, the point (.5, 2.25) maximizes the objective function.

** 1. Simplex Method:
**By far the simplest method for solving simplex problems is with
a calculator program. Later,

I'll give you a location on my

Ex 1:

as follows:

z=3x

2x

2x

2x

x

z=3x

2 1 1 1 0 0 |150

2 2 8 0 1 0 | 200

Now, we want to solve this simplex problem. Using the Matrix operations, do that as follows:

a) Press 2ND, MATRIX, move the cursor to EDIT and press ENTER.

b) Change the dimensions to 4 x 7 and enter the values into the matrix. Just enter the number and

press ENTER to do that.

c) After you have completed entering the information, press 2ND, QUIT to go the home screen.

d) Just as a precaution, let's store this in matrix [B] just so we won't have to re-enter everything

in case we make a mistake. So, press 2ND, MATRIX, ENTER, 2ND, MATRIX, 2(B). You should now

have [A]→[B] displayed on the screen. Press ENTER and the storing will take place and the matrix

will be displayed.

e) Now, we want to decide where to pivot. Since -3 is the most negative number, select that column.

Now, divide each number in that column into the numbers at the end. The first number gives

150/2=75, which is smaller that the other quotients. So, we will pivot on that point.

positions in that column. The syntax of the Operation that we will use is as follows:

cc→M:c→A:c→R:*row+(M, [A], A,R)→[A], where c is a character (number, minus sign, etc.) , M is the

row multiplier, A is thenumber of the row being multiplied, and R is the row being replaced.

Remember that the arrow indicates pressing the STO key, the colons are obtained by pressing

ALPHA and the decimal key, and *row+( is obtained by pressing 2ND, MATRIX, moving the

cursor to MATH, scroll down to *row+( and pressing ENTER. The matrix symbol [A], must be

obtained by pressing 2ND, MATRIX, ENTER.

f) Now, let's do row 2. We will the following on the home screen:

-1→M:1→A:2→R:*row+(M, [A], A,R)→[A]. Press ENTER and a zero will appear in the appropriate

cell with the other cells in row two modified accordingly.

g) We want a zero in place of the 2 in row 3. Press 2ND, ENTER and edit the number for R, so that you

now have this: the display so that it

reads as follows: -1→M:1→A:3→R:*row+(M, [A], A,R)→[A]. Press ENTER and the changed

matrix will be displayed.

h) We want a zero in place of the -3 in row 4. Press 2ND, ENTER and edit the numbers for M and R,

so that you have this: 3/2→M:1→A:4→R:*row+(M, [A], A,R)→[A]. Press ENTER and the changed

matrix will be displayed.

reads as follows: *row+(3/2, [A], 1, 4)→[A].

i) We want to reduce the first number, 2 to 1. Normally, we would use the multiply row function to

do that, but to reduce key strokes, we're going to do it another way. So, press 2ND, ENTER and

edit the display so that it reads as follows: -1/2→M:1→A:1→R:*row+(M, [A], A,R)→[A]. Press

ENTER and the following will be displayed.

[[ 1 .5 .5 .5 0 0 75]

[ 0 1 7 -1 1 0 50]

[0 2 0 -1 0 1 17]

Now, the pivot point will be on the 1 in column 2.

j) We want a zero in place of the 2 in row 3 Column2.. Press 2ND, ENTER and edit the numbers for M,

and R, so that you have this: -2→M:2→A:3→R:*row+(M, [A], A,R)→[A]. Press ENTER and the changed

matrix will be displayed

k) We want a zero in place of the .5 in row 1, column2. Press 2ND, ENTER and edit the numbers for M and R,

so that you have this: -.5→M:2→A:1→R:*row+(M, [A], A,R)→[A]. Press ENTER and the changed

matrix will be displayed.

l) We want a zero in place of the -.5 in row 4, column 2. Press 2ND, ENTER and edit the numbers for M and R,

so that you have this: .5→M:1→A:4→R:*row+(M, [A], A,R)→[A]. Press ENTER and the changed

matrix will be displayed.

Since there are no more negative numbers in the last row, the solution is now complete. The solution

you should have is as follows:

[[ 1 0 -3 1 -.5 0 50]

[ 0 1 7 -1 1 0 50]

[0 0 -14 1 -2 1 70]

**VI. Calculus Applications**:

**1. Cost, Average Cost, and Marginal:
** Suppose that a company estimates that the cost (in dollars) of
producing x units of a certain product is given by

C(x) = 200+0.05x+0.0001x².

Cost of producing 500 units.

a) Press Y= and enter the equation 200+.05x +.0002x². Use the [X,T,0,n] key to enter x and the x² key to

enter the exponent after entering x.

Press WINDOW and set Xmin at 450; then press ZOOM, 0 (ZoomFit) display the graph.

b) Press 2ND, CALC, ENTER.

c) From the displayed graph screen enter 500 opposite s and press ENTER. The cost of 250 will be displayed.

Average cost of producing 500 units.

a) Press Y= and change the entry so tha tit is as follows: (200+.05x +.0002x²)/x

Press WINDOW and set Xmin=450; then press ZOOM, 0(ZoomFit) to display the graph.

b) Press 2ND, CALC, ENTER and enter 500 opposite x.

c) Press ENTER and x=500, y=.5 will be displayed. The average cost is $0.50.

Marginal Cost for 500 Units:

a) Change the equation back to the cost equation: 200 +.05x+ .0001x².

b) From the graphing screen press, 2ND, CALC, 6(dy/dx).

c) Enter 500 and press ENTER. The equation dy/dx =.15 will be displayed.

**2. Average-Cost Minimization:
**Find the number of units that will minimize the average cost
and the corresponding cost.

We want to find the point where C(x) = C'(x), so we'll need the first derivative: c'(x)=.05+.0002x.

a) Enter (200+.005x+.0001x²)/x opposite Y1 and .05+.0002x opposite Y2.

b) Set x-min = 450 and x-max = 200. Press ZOON, 0(ZoomFit) to display the graphs.

Now find the intersection point.

c) Press 2ND, Calc, 5 (intersect).

d) From the graph screen, press ENTER, ENTER; then move the cursor approximately to the intersection

and press ENTER again.

e) The numbers x=1414.21... and y=.332... will be displayed. So, the number to minimize average cost

is approximately 1414 and the cost is approximately .332 dollars.

** 3. Cost
Minimization;
** The cost C(x) of manufacturing x units of a produce is
approximated by the following: C(x) =100+10/x+x²/100.

Find the number of units that should be manufactured to minimize cost.

a) Press Y= and enter the equation 00+ 10/x + x²/100. Use the [X,T,0,n] key to enter x and the x² key to

enter the exponent after entering x. Press WINDOW and set Xmin =0, Xmax=50, Ymin=90 and Ymax =140.

b) Press 2ND, CALC, 3 (minimum), and move the cursor to the left of the minimum (about 5) and press ENTER.

Move the cursor to the right of the minimum (about 20) and press ENTER. Move the cursor back to the left

to approximately the minimum and press ENTER. The value 10 will be displayed for the number to minimize

cost.

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