> 02/ .bjbj .L&+\0pj0l0l0l0l0l0l0w25rl0l00j0j0".*0EsF.V0000.85.50*05*0,l0l0(05 : Activity for Pre-Calculus
Unit: Exponential & Logarithmic Family
The U.S. economy is in shambles, and the future of the nations Social Security system is bleak. Currently, workers pay 7.65% of their earnings to Social Security and Medicare, and their employers match this. This money is distributed to approximately 45 million retired people, and this number will grow significantly when the baby boomers retire within the next decade or so. In addition to the record number of retirees, life expectancy is increasing, further driving up the cost of Social Security. It is estimated that, in 2018, the benefits paid out will exceed the contributions coming in (in other words more money will be going out than coming in). While there is disagreement about how large the problem is, it is generally accepted that the benefits paid to young workers will be greatly reduced (some say as much as 56%) when they retire.
Several years ago, President Clinton listed three possibilities to alleviate the problems with Social Security significantly increase taxes, decrease benefits, or privatize investments. Workers already pay out about 30% of their paychecks to taxes, so increasing the tax burden would further reduce consumer spending. The rate of poverty amongst the elderly is appallingly high, so decreasing benefits is also out of the question. President Bush promoted privatizing investments (i.e. retirement money is invested in the stock market). Today, the federal government grants tax breaks for those who save money for retirement, but privately saving money for retirement is still optional. While economists have suggested other cures for the ailing Social Security system, it is unwise to rely solely on Social Security benefits. Everyone should have an alternate retirement plan, like savings accounts and stock investments.
In this unit, we will use the various financial formulas to calculate interest on savings accounts, credit cards, and loans. We will also explore investments in the stock market.
Directions:
For the Exploration below, you will only collect data. The data will be used for a mini-project later in the unit. This activity and its final product must be completed individually. Only work written legibly in pencil will receive full credit.
Exploration:
Choose a company (or companies) in which you would like to invest money. Go to http://finance.yahoo.com, type in the name of your company in the search box, and choose the most appropriate stock from the drop-down list. When you find the company, write down the abbreviation on your chart, and press the Get Quotes button.
You have a maximum of $10,000 at your disposal. Spend it wisely. Part of your grade will be determined by your net loss/gain of your investment(s). The price you record on the first day is the original buying price for 1 stock, and the price you record on the last day is your selling price for 1 stock. Remember that stocks can only be bought in packets of 100. (For example: If the buying price is $22, you will only be able to buy at most 400 stocks for $8800.)
When you come into class each day for the next two weeks or so, check your stock for the current value of your company stock. Record daily the specified information in the accompanying chart. If you have more than one company, you will need to have a chart for each company. If you miss a day of school, you are still responsible for that days information.
Activity for Pre-Calculus
Unit: Exponential & Logarithmic Family
Directions:
Complete the Exploration below. You will need the data that you collected in the previous activity. This activity and the poster must be completed individually.
Exploration:
Using Excel, make a spreadsheet with the headings below. Use the information you recorded in the Introduction chart. Add extra Value columns and Net Loss/Gain column for each additional investment.
DateValue (single stock)Value (all stocks)Net Loss(-)/Gain(+) (all stocks)Value of All Investment(s)
For each company in which you invested, make a line graph that compares the date (x-axis) and the single stock value (y-axis).
Make a line graph that compares the date (x-axis) and the value of all investments (y-axis).
Make sure all graphs and the chart are neat before printing them out. (Graphs and charts that are not neat and labeled will not receive full credit.)
Type a paragraph summarizing and analyzing your investment. (Was it a good or bad investment? How would you modify future investments? Is investing short-term better than long-term? et cetera)
Make a poster that includes your Excel chart, graphs, and paragraph. Glue the original chart to the back of the poster.
Your final grade will be based on the accuracy of your charts and graphs, the overall neatness of the poster, the creativity of the poster design, the smartness of your investments, and the depth and breadth of your paragraph.
Group Lab for Pre-Calculus
Unit: Exponential & Logarithmic Family
Section 3-4
Directions:
Please complete the Explorations below. After your group has completed the Explorations, answer the Discussion questions. Printed copies of the three Excel spreadsheets and the answers to the Discussion questions can be turned in as a group assignment (i.e. turn in only one copy with the names of participating group members). Only work written legibly in pencil will receive full credit.
Exploration 1:
In Excel, create a spreadsheet like the one below:
YearPrincipal (start of year)Interest AccruedAccount Balance (end of year)1$5002320
For an investment (or loan) that is compounded annually, the simple interest formula is used to calculate the interest accrued for just that year (i.e. t = 1), the interest is added to the principal to create the end-of-year account balance, and finally the account balance becomes next years principal. Use this method in the Excel sheet to find the account balance of a $500 investment with a 2% interest rate for 20 years. (Hint: Use formulas, so that you will not have to recalculate for each year).
Print out a copy of this chart before moving on to the next step.
Increase the initial principal to $1000, and find the new account balance at the end of 20 years. If you set up the formulas properly, the other values should change automatically.
Print out a copy of this chart before moving on to the next step.
Change the initial principal back to $500. Increase the annual interest rate to 4%, and find the new account balance at the end of 20 years. (The values will not automatically change; you will probably have to change the formulas.)
Print out a copy of this chart.
Discussion 1:
Using the simple interest formula, calculate the interest accrued and the account balance of a $500 investment with a 2% annual interest rate for 20 years.
Using the compound interest formula, calculate the interest accrued and the account balance of a $500 investment with a 2% annual interest rate for 20 years. How did this compare to the account balance you found using the spreadsheet?
Why do the two values you calculated in questions #1 and #2 differ?
What produced the larger account balance doubling the initial investment or doubling the interest rate? If you had the choice, would you rather double your initial investment or the annual interest rate? Why?
Write a recursive formula to describe the process you used in Excel. Be sure to define the variables. (Formulas without the variables defined will not receive full credit.)
The compound interest formula can be used to describe population growth over time. For each of the variables in the compound interest formula, tell what its population growth counterpart might be.
In 1950, the world population was 2,555,898,461. From 1950 to 1951, the population increased 1.45%. If the population kept increasing at that rate, what would be the population today?
Currently the world population is about 6.65 billion. How does this compare with the number you calculated above? What does this mean about the values of the formula? What does this mean about the world population?
Exploration 2:
Assuming there are 365.25 days in a year, use the compound interest formula to fill out the accompanying chart. Assume that the initial investment is $500 and the interest rate is 2%.
With the formulas you have learned at this point, you will not be able to find an exact account balance for an investment whose interest is compounded continuously. However, using the other account balances, you should be able to give a close estimate.
Discussion 2:
Do you think the account balance approaches a limit? If so, approximate this limit. If not, explain why there is no limit.
Fill in the variables in the compound interest formula with actual numbers for an investment of $1000 at 3% interest rate compounded continuously for 10 years.
Why is this formula useless?
Group Lab for Pre-Calculus
Unit: Exponential & Logarithmic Family
Section 3-4
Directions:
Answer the Discussion questions below. The answers to the Discussion questions can be turned in as a group assignment (i.e. turn in only one copy with the names of participating group members). Only work written legibly in pencil will receive full credit.
Discussion:
What is the value of e2, accurate to four decimal places?
What is the approximate value of EMBED Equation.3 , accurate to four decimal places?
What is the value of e3, accurate to four decimal places?
What is the approximate value of EMBED Equation.3 , accurate to four decimal places?
Rewrite EMBED Equation.3 in terms of e.
Rewrite EMBED Equation.3 in terms of e.
Rewrite EMBED Equation.3 in terms of e.
The account balance of an investment can be calculated using the formula EMBED Equation.3 . What are the details of this investment (i.e. principal, annual interest rate, type of interest, and term)?
!ACDAE@jlmqyzlyDABK]
_i
&5i"%"W&e&f&''))***+#+$+0+ɾhc5OJQJ\ hc\hI6HhI6H6 hq5 hI6H6 hc6hI6Hhc6hchI6H hc5 hI6H5KD89AyklyCDI^$$Ifa$gd(p
&F gdI6HgdI6H
&F^q83gdI6Hkd$$IfTlrd$<$ p$ t
t0644
layt(pT$$Ifa$gd(p/"[\A]%&5hin $$Ifa$$a$
&FgdI6H
&F gdI6HZQQQQ $$Ifa$kd$$IfTl\4$X
t0644
laTZQQQQ $$Ifa$kd$$IfTl\4$X
t0644
laTZQQQQ $$Ifa$kdh$$IfTl\4$X
t0644
laTZQQQQ $$Ifa$kd*$$IfTl\4$X
t0644
laTZQQQQ $$Ifa$kd$$IfTl\4$X
t0644
laT !!""ZXSSSSSSX
&Fkd$$IfTl\4$X
t0644
laT "%""##$p%5&&'''()))*****+#+$+0+0,1,=,gdI6H
&F
&F
&F0+;+E+j+t+,,1,=,R,S,T,,,,,,,,,,--.-A-B-C-D-o-p------------------jZ
hcEHUjH
hcCJUVaJj
hcEHUjH
hcCJUVaJjhcEHUjH
hcCJUVaJjphcEHUjH
hcCJUVaJjhcU hcH* hc5 hc6hc-=,w,,-g----...gdI6H
&F
------=.>.Q.R.S.T..ƼjhcEHUjiH
hcCJUVaJ hc6hcjhcUjhcEHUjH
hcCJUVaJ,1h/ =!"#$%$$If!vh5<5$ 5p5$ 5t#v<#v$ #vp#v$ #vt:Vl
t06,5<5$ 5p5$ 5tyt(pT$$If!vh5X5
55
#vX#v
#v#v
:Vl
t065X5
55
T$$If!vh5X5
55
#vX#v
#v#v
:Vl
t065X5
55
T$$If!vh5X5
55
#vX#v
#v#v
:Vl
t065X5
55
T$$If!vh5X5
55
#vX#v
#v#v
:Vl
t065X5
55
T$$If!vh5X5
55
#vX#v
#v#v
:Vl
t065X5
55
T$$If!vh5X5
55
#vX#v
#v#v
:Vl
t065X5
55
TDd
\
c$A??#"`2
g˂S=I5`!
g˂S=I
xcdd``$d@9`,&FF(`TMRcgbR vNznĒʂT@_L ĺE'X@+ȝ>}V9@& Ma`%^AaǒXkyZ6LF]F\@Z5* yL`~@27d&\PsA,@sC2sSRspb.OgUB:LkYl |t{H?AmG9
JN(
ra =F~;|$6F022)G
>X4
K3aXM\|(`padbR
,.IeԡRYO`cDd
\
c$A??#"`2գ
~)?c[5`!գ
~)?c
xcdd``$d@9`,&FF(`TMRcgbR znĒʂT@_L ĺE'X@+ȝ>}V9@& Ma`( İc@`܁? LF]F\@Z5* 'ņ<&[?
2Bj Q!
~
Ay8 1 j{3`s*!|,L>$ً`{6#\t`a%'oL9@Ӱ# #3zʱm.0ML+8erA88b;s+KRsaPdk),Ā'f~徂Dd
\
c$A??#"`2ڒEUmԂ ʌ=5`!ڒEUmԂ ʌ=p
xڕR=OA;P#101B(-&ѐ먵h@bsvo%{͛7ovA@2`
!c1t]W%6.ݸRf:L˃!J~P,Q|XD`;uztr@FTEq>+lE}M$d@9`,&FF(`TYCRcgbR vv@P5<%!8 :@u!f0%0X@-6;3}rȁL@(\%ZAaǒXk3vqg|ҪQIȼP.m1l #4*geZZӝs~b(`W 0!#"(-D⎆X`d?, \t-`po6gaX 0)'o9@ӹi3@\#F&&\ :@Dg!t_3}
!"#$%&()*+,-.?1456879:;=<>BC@ADFGHIJKLMNOPQRSTUVWXYZ[\]^_Root Entry# F`is3
Data
'WordDocument".LObjectPool% ~~sOle
CompObjfObjInfo"%'()*+,./013
FMicrosoft Equation 3.0DS EquationEquation.39qdT'
'limn!"
1+2n
()n
FMicrosoft Equation 3.0DS EqEquation Native _1217784795F>s>sOle
CompObj
fuationEquation.39qdP;
'limn!"
1+3n
()n
FMicrosoft Equation 3.0DS EquationEquation.39qObjInfo
Equation Native
_1217784831F>s>sOle
CompObj
fObjInfoEquation Native _1217785284F>s>sdh
'limn!"
1+rn
()n
FMicrosoft Equation 3.0DS EquationEquation.39ql#|
'limn!"
251+rn
()Ole
CompObjfObjInfoEquation Native n
FMicrosoft Equation 3.0DS EquationEquation.39qv(=
'limn!"
P0
1+rn
()n_1217785311F>s>sOle
CompObjfObjInfoEquation Native _1217785961F>s>sOle
CompObj !f
FMicrosoft Equation 3.0DS EquationEquation.39q>.
P=750e.015tOh+'0\
ObjInfo!#Equation Native $Z1TableE5SummaryInformation($&)Dd
\
c$A??#"`2
b2y?ϕE5`!b2y?ϕ xڥKAUWC:Du:D/HS):d$):w٠n-H.?&u(lDVYfxo~>^)tQ`N/XHZŭ92$|8?yTjMC&t>4'bE@1=B+D&?!4$*yV|Lo3g<:ۼD?ڎZ7=Mg2?LfEO=
^s@ݔq:~/ Ϸo}A韤ϾuP$ʊ"+W0A_ipit^mkC;~j8Syc;=ƽJxꡬBS?$
0<DLTDirections for SIMMS IVKarmaNormal.dotmskittell4Microsoft Office Word@H'@X'@LUr@Ts ՜.+,0hp
Hewlett-PackardFDocumentSummaryInformation8-<CompObj2y&Directions for SIMMS IVTitle
F'Microsoft Office Word 97-2003 Document
MSWordDocWord.Document.89q^2 0@P`p2( 0@P`p 0@P`p 0@P`p 0@P`p 0@P`p 0@P`p8XV~_HmH nH sH tH @`@NormalCJ_HaJmH sH tH DA DDefault Paragraph FontVi@VTable Normal :V44
la(k (No List6U6 Hyperlink>*B*phPK![Content_Types].xmlj0Eжr(Iw},-j4 wP-t#bΙ{UTU^hd}㨫)*1P' ^W0)T9<l#$yi};~@(Hu*Dנz/0ǰ$X3aZ,D0j~3߶b~i>3\`?/[G\!-Rk.sԻ..a濭?PK!֧6_rels/.relsj0}Q%v/C/}(h"O
= C?hv=Ʌ%[xp{۵_Pѣ<1H0ORBdJE4b$q_6LR7`0̞O,En7Lib/SeеPK!kytheme/theme/themeManager.xmlM
@}w7c(EbˮCAǠҟ7՛K
Y,
e.|,H,lxɴIsQ}#Ր ֵ+!,^$j=GW)E+&
8PK!Ptheme/theme/theme1.xmlYOo6w toc'vuر-MniP@I}úama[إ4:lЯGRX^6؊>$!)O^rC$y@/yH*)UDb`}"qۋJחX^)I`nEp)liV[]1M<OP6r=zgbIguSebORD۫qu gZo~ٺlAplxpT0+[}`jzAV2Fi@qv֬5\|ʜ̭NleXdsjcs7f
W+Ն7`gȘJj|h(KD-
dXiJ؇(x$(:;˹!I_TS1?E??ZBΪmU/?~xY'y5g&/ɋ>GMGeD3Vq%'#q$8K)fw9:ĵ
x}rxwr:\TZaG*y8IjbRc|XŻǿI
u3KGnD1NIBs
RuK>V.EL+M2#'fi~Vvl{u8zH
*:(W☕
~JTe\O*tHGHY}KNP*ݾ˦TѼ9/#A7qZ$*c?qUnwN%Oi4=3ڗP
1Pm\\9Mؓ2aD];Yt\[x]}Wr|]g-
eW
)6-rCSj
id DЇAΜIqbJ#x꺃6k#ASh&ʌt(Q%p%m&]caSl=X\P1Mh9MVdDAaVB[݈fJíP|8քAV^f
Hn-"d>znǊ ة>b&2vKyϼD:,AGm\nziÙ.uχYC6OMf3or$5NHT[XF64T,ќM0E)`#5XY`פ;%1U٥m;R>QDDcpU'&LE/pm%]8firS4d7y\`JnίIR3U~7+#mqBiDi*L69mY&iHE=(K&N!V.KeLDĕ{D vEꦚdeNƟe(MN9ߜR6&3(a/DUz<{ˊYȳV)9Z[4^n5!J?Q3eBoCMm<.vpIYfZY_p[=al-Y}Nc͙ŋ4vfavl'SA8|*u{-ߟ0%M07%<ҍPK!
ѐ'theme/theme/_rels/themeManager.xml.relsM
0wooӺ&݈Э5
6?$Q
,.aic21h:qm@RN;d`o7gK(M&$R(.1r'JЊT8V"AȻHu}|$b{P8g/]QAsم(#L[PK-![Content_Types].xmlPK-!֧6+_rels/.relsPK-!kytheme/theme/themeManager.xmlPK-!Ptheme/theme/theme1.xmlPK-!
ѐ' theme/theme/_rels/themeManager.xml.relsPK]
&L0+-.#%^"=,. !"$$$$-%A%C%o%%%%%%%%%=&Q&S&&::::::8@0(
B
S ?""&""$$*%-%5&=&&3333!ACCAEYjlm
+
7
7
8
@
z
"##$$-%D%o%%%%%%=&T&&&&&!ACCAEYjlmz
"##$$-%D%o%%%%%%=&T&&&& Jk@}C>D&@&3Oyk2n5XB%@>Hw[K]gAKFq_5h
^`hH.h
^`hH.h
pLp^p`LhH.h
@@^@`hH.h
^`hH.h
L^`LhH.h
^`hH.h
^`hH.h
PLP^P`LhH.h
^`hH.h
^`hH.h
pLp^p`LhH.h
@@^@`hH.h
^`hH.h
L^`LhH.h
^`hH.h
^`hH.h
PLP^P`LhH.h
^`hH.h
^`hH.h
pLp^p`LhH.h
@@^@`hH.h
^`hH.h
L^`LhH.h
^`hH.h
^`hH.h
PLP^P`LhH.h
^`hH.h
^`hH.h
pLp^p`LhH.h
@@^@`hH.h
^`hH.h
L^`LhH.h
^`hH.h
^`hH.h
PLP^P`LhH.h
^`hH.h
^`hH.h
pLp^p`LhH.h
@@^@`hH.h
^`hH.h
L^`LhH.h
^`hH.h
^`hH.h
PLP^P`LhH.h
^`hH.h
^`hH.h
pLp^p`LhH.h
@@^@`hH.h
^`hH.h
L^`LhH.h
^`hH.h
^`hH.h
PLP^P`LhH.h
^`hH.h
^`hH.h
pLp^p`LhH.h
@@^@`hH.h
^`hH.h
L^`LhH.h
^`hH.h
^`hH.h
PLP^P`LhH.h^`OJQJo(hHh^`OJQJ^Jo(hHohpp^p`OJQJo(hHh@@^@`OJQJo(hHh^`OJQJ^Jo(hHoh^`OJQJo(hHh^`OJQJo(hHh^`OJQJ^Jo(hHohPP^P`OJQJo(hHh
^`o(hH.h^`OJQJ^Jo(hHohpp^p`OJQJo(hHh@@^@`OJQJo(hHh^`OJQJ^Jo(hHoh^`OJQJo(hHh^`OJQJo(hHh^`OJQJ^Jo(hHohPP^P`OJQJo(hH Jk%@Oyk2&@&n5}Cw[K]KFq_>H cI6H(pq &&@&@UnknownG*Ax Times New Roman5Symbol3.*Cx Arial;.*Cx Helvetica?= *Cx Courier New;WingdingsACambria Math"h82gF2gRئ F F$24d&&+3qHP?c2!xxDirections for SIMMS IVKarmaskittell0 ~~