1. Add three consecutive letters of the alphabet to the group of letters below, without splitting the consecutive letters, to form another word. DY

2. STUDY

3. Which month comes next?
January, March, June,
October, March, ?

4. September

5. All widgets are green. Everything green has a hole in the middle
All widgets are green. Everything green has a hole in the middle. Some things that are green have a jagged edge. Therefore:
All widgets have a hole in the middle
Everything with a jagged edge is a widget.
Neither of the above is true.
Both the above are true.

6. 1. All widgets have a hole in the middle

7. Exponential Modeling
Week 2

8. Review: linear equations
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
How much does she make after selling 10 more boxes?
y = 2.60 (10) = $41.60

9. Review: linear equations
How many boxes does she have to sell to make $130? (y = 2.60x )
130 = 2.60x
(subtract from both sides)
= 2.6x
(divide both sides by 2.6)
x = 44

10. Review: linear equations
y=5x-9
Solve for y when x = 2.
y = 5(2)-9
y = 1
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

11. Last week… We learned about linear modeling. Model: y = mx +b
Graph: straight line

12. This week…
Exponential Modeling
x is an exponent.

13. This week… Exponential growth Exponential decay Model: Model:
y = a(1+r)x
y: final
a: initial
r: rate
x: time
Model:
y = a(1-r)x
y: final
a: initial
r: rate
x: time

14. Graph:

15. Examples of Exponential Growth
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

16. Difference: How can you tell? 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

17. Percent Change example
exponential growth?

18. Percent Change example

19. Percent Change example

20. Percent Change example
The percent change is 20% each time. So it is an exponential function.

21. Exponential Modeling Example
Two bosses
A: one million dollars for one month
B: a penny doubled every day for a month
Who would you work for?

22. Exponential Modeling Example
Boss B
Day 1: $.02
Day 2: $.04
Day 3: $.08 …
Day 10: $10.24
Day 20: $10,485.76
Change of mind?

23. Exponential Modeling Example
Calculations
y = a (1+r)x
y = .01 (1+1)30
y = 10,737,418.24

24. Exponential Modeling Growth (savings account)
y = a(1+r)x
Decay (radioisotope dating)
y = a(1-r) x

25. Exponential Growth -- Excel
If roaches grow at a rate of 25% every 10 days, how long will it take 400 roaches to become 1000 in number?

26. Exponential Growth -- Excel

27. Exponential Growth -- Excel

28. Exponential Growth -- Excel
Drag it down
Right click on the + at the right bottom
Move down with the mouse

29. Exponential Growth -- Excel

30. Exponential Growth -- Excel
A little bit after 40 days

31. Exponential Decay -- Excel
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?

32. Exponential Decay -- Excel
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)

33. Exponential Decay -- Excel

34. Exponential Decay -- Excel

35. Exponential Decay -- Excel
Answer: between 2000 to 2100 years old

36. Assignments:
Activity 2, 3
Homework 2