Simple and Compound Interest

Simple- interest that gets calculated a grand total of one time

compound- interest is calculated continuely at the end of every compounding period

Interest:
(think 2 perspectives)
* lend .......... * borrow.
(invest) .......
*to bank ..... *from bank
give ......... get

An amount of money generated through the use of 3 variables:
PRINCIPAL AMOUNT(P)$
INTEREST RATE (r)%
TIME (t)years

SIMPLE
I=(P)(r)(t)

COMPOUND
A=1(P+r/n)n(t)

P=principal
r=rate
t=time
n=number of compoundings per year
I=interest (by itself)
A=amount(principal plus interest)




Example

Bob invests money. He starts with $1000.00. He invests it at 5% interest. He invests only 1 year at a time, but every year he decides to reinvest his interest. Calculate the value of his investment at the endof 5 years.

^^ simple interest(5 times).
I=Prt

I=?
P=1000
r=0.05
t=1

1.....I=Prt
=(1000)(0.05)(1)
=$50
at end of 1st year, he earns $50.

2.....
I=Prt
=(1050)(0.05)(1)
=$52.50

3.....
I=Prt
=(1102.50)(0.05)(1)
$=55.13

4.....
I=Prt
=(1157.63)(0.05)(1)
=$57.88

5.....
I=Prt
=(1215.51)(0.05)(1)
=$60.78

Total value of his investment:
$1276.29
^^ this is the compounded amount
(interest was added.. (compounded)
to the principal each time).

OR ..
once through this formula.

A=P(1+r/n)n(t)
A=1000(1+0.05/1)(1)(5)
A=1000(1.05)^5
A=1276.28

Hmmmm.... remember this ..
y=a*b^x

Linear inqualities

Linear Inequalities (Graphing RULES with LOGIC TESTING)

Consider this:
-8x + 4y - 3 >= 0

What do i do with this without graphmatica?

4y>= 8x +3
y >=2x+3/4

similar to y= mx+b
y= 2x +3/4

I kno that the corresponding linear equation, goes through (0,3/4) and that the line has slope 2.

Linear Programming

Linear Programming

We start by understanding that:

1) Equations create linear/non linear "curves"

****2) inequalities create "plane boundaries".

{shaded regions}

OPEN VS CLOSE

boundaries

< > <>

an open circle number line a filled in dot

dotted line plane solid line

Linear programming is concerned with the answers to the questions of "Where do the boundaries of the open or closed regions intercept".

A pet store farmer has turtles and rabbits. He has room for only 100 pets. He can sell turtles for $10 each and rabboits for 30 bucks each. He decides that he must earn at least 1500 bucks to make the job worthwhile.

a) Write the inequality that respresents the total of pets?

b)Write the inequality of that represents the total profit?

c) Graph these inequalities.

d)What are some possible solutions for the farmer?

a) T + R <(less then or equal to) 100.

b)10y+30x >(greater than or equal to)

d) (25,75) ;; (100, 0) Get rid of the turtles. The rabbits make more money.

Whats on the test?

1 . Mechanics
- functions and relations
- domain/range (x+y display graphs as proof)
- calculator stuff
(tracing, evaluating, windows, zooms, tables, graphs... etc.)


2. Quadratics

y-k=a(x-h)^2 form..
=(h,k) vertex
a ..determines opening..

OR..

y=ax^2 + bx + c Standard form.

- symmetric
(about the axis of symmetry)
y=ax^1 - linear
y=ax^2+bx -quadradic
y=ax^3+bx^2+cx -cubic

2 kinds of questions..
a) your given the function, answer questions
b) given table of values ; DO regression from the stat plot QUADREG

• USE ANY STRATEGY TO SHOW WORK TO RECEIVE MARKS!!

- Excel, Graphmatica, Calculator etc.

3. Cubics
*box volume or relative min./max problems

up...... minimum.

down.... maximum.

**on cubic functions, there is a RELATIVE maximum and a RELATIVE minimum.


4. Exponentials

no e questions

WILL have to use EXPREG to create y=a.b^x

Corrections. Questions.

10.

t = time
h(t) =147t-16t^2

put that in graphmatica
change window settings

when does the ball reach the height?
337.6ft at 4.6 seconds.

When does it hit the ground again?
9.2 seconds, times 4.6 times 2. parabla
Symmetry


~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

11.

y=4x/3 - x^2/90

Back to graphmatica, put the y= thing in..
graph should show up.

Whats the max height of the football?
40 feet

How long far does it go to hit the ground?
120 feet

Will the football fall into the crossbar?
its kicked from the 35 yrd line, (35 x 3) = 105 ft.
But, The kick is successfull.

How far would the ball be above the crossbar?
2.5 feet.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
12.

total revenue = (# of fares###)(#cost per ride$$$)

Let x= # of $1 fare increases
Let y = total revenue of $

y= (300-15x)(10+x)
Check the blogs....
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Precalculus thinking

This is what we do, Applied.
Area = Length * Width
- - makes sense right?

Precalculus find out whut the width is, and they know what the length is, so basically they come out with an equation like this..
y= (24-2x)(x)
y= 24 x-2x squ.
y= -2x squ. +24x

Assignment/Lil bit of notes.

Ex.1 (handout)
For monday : Pg A-4; 3,4,5

3 c) y=x^2+6x+4 --- this has a minimum(the bottom of the cup)
::to find vertex for sure

2nd.. trace.. minimum.

MAXIMUM.. DOWN..
MINIMUM UP..

Random Notes..

x 1 - linear

x2 - quadratic

x3 - cubic

x4 - quartric

x5 - quintic

NON LINEAR

A)Domain and Range
B)Function
C)Quadratic functions
D)Cubic functions

Do not post material to the blog without referencing!

.. stay in secondary school. Things in highschool.
Keep references, examples, images, videos, links, etc. SIMPLE.
You're teaching grade 11 classmates.

Be creative!

By the end of Fridays class, you should be able to answer questions like::
What is a function??
What is the domain of the pictured function?? Why?
Compare quadratic functions to cubic functions? etc.........