Transcript 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
for $2.60 a box. She’s already made
$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
learned about linear modeling.
• 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)
Radioactive substances decay exponentially
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
(radioisotope dating)
• 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
Dead
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
the Dead Sea Scrolls?
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)
Answer: between
2000 to 2100 years old
Activity
2, 3
Homework 2