### Growth

``` Add
three consecutive letters of the
alphabet to the group of letters below,
without splitting the consecutive letters,
to form another word.
DY
STUDY
 Which
month comes next?
January, March, June,
October, March, ?
September
 All
widgets are green. Everything green
has a hole in the middle. Some things that
are green have a jagged edge. Therefore:
1. All widgets have a hole in the middle
2. Everything with a jagged edge is a widget.
3. Neither of the above is true.
4. Both the above are true.
1. All widgets have a hole in the middle
Week 2
 Your
sister is selling Girl Scout cookies
\$15.60.
 Write
an equation for the situation above:
• y = 2.60x + 15.60
 How
much does she make after selling 10
more boxes?
• y = 2.60 (10) + 15.60 = \$41.60
 How
many boxes does she have to sell to
make \$130? (y = 2.60x + 15.60)
• 130 = 2.60x + 15.60
• (subtract 15.60 from both sides)
• 114.40 = 2.6x
• (divide both sides by 2.6)
• x = 44
 y=5x-9
 Solve for y
• y = 5(2)-9
• y=1
when x = 2.
 Solve for x when y = 6.
• 6 = 5x – 9 (next: add 9 to both sides)
• 15 = 5x (next: divide both sides by 5)
• x=3
 We
• Model: y = mx +b
• Graph: straight line
 Exponential
Modeling
x is an exponent.
EXPONENTIAL GROWTH

Model:
y = a(1+r)x




y: final
a: initial
r: rate
x: time
EXPONENTIAL DECAY

Model:
y = a(1-r)x




y: final
a: initial
r: rate
x: time
 Graph:








Populations tend to growth exponentially not linearly
When an object cools (e.g., a pot of soup), the temperature
decreases exponentially toward the ambient temperature (the
surrounding temperature)
Bacteria populations grow exponentially
Money in a savings account with at a fixed rate of interest
increases exponentially
Viruses and even rumors tend to spread exponentially through
a population (at first)
Anything that doubles, triples, halves over a certain amount of
time
Anything that increases or decreases by a percent

Difference:
• Linear: Constant Rate of Change
• Exponential: Constant Percent Change

How can you tell?
• Linear, if it increases by the same or decreases by the
same
• Exponential, calculate the percent change and see if it
stays constant
 Percent change = (changed- reference)/reference
 exponential
growth?
 The
percent change is 20% each time. So
it is an exponential function.
 Two
bosses
• A: one million dollars for one month
• B: a penny doubled every day for a month
 Who
would you work for?
 Boss B
• Day 1: \$.02
• Day 2: \$.04
• Day 3: \$.08
• …
• Day 10: \$10.24
• …
• Day 20: \$10,485.76
 Change of mind?
 Calculations
• y = a (1+r)x
• y = .01 (1+1)30
• y = 10,737,418.24
 Growth
(savings account)
• y = a(1+r)x
 Decay
• y = a(1-r) x
 If
roaches grow at a rate of 25% every 10
days, how long will it take 400 roaches to
become 1000 in number?
 Drag
it down
• Right click on the + at the right bottom
• Move down with the mouse
A
little bit after 40 days
Sea Scrolls have about 78% of the
normally occurring amount of Carbon 14
in them. Carbon 14 decays at a rate of
about 1.202% per 100 years. How old are
 Since
we know the rate of decay per
every 100 years, make the excel table
have intervals of 100 years.
(after entering 0 and 100, you can select
the two and drag down)