0. Question One: https://lh6.googleusercontent.com/QNdVk7rTf73lvVfdKOZ2QF4FKqsDf_BfhmPPikrge-C5gSre6wi9YfZqZJE9f38DURr-DsxaGLsKftq2Bb-Y0ntUAFNgfnZFP-ldubgouUf-2gsntrg
from: (no peeking!): http://ccssimath.blogspot.com/2012/06/concept-of-area-part-3.html
then: http://ccssimath.blogspot.com/p/blog-page_9813.html
Entrance Question: Dice
Creation of an exponential function.
New Pattern
f(x)=ab^x
How would it look if we did it with dice?
define the pattern we want to use
sample(1:6,1,replace=TRUE)
What do these graphs look like?
a
b
Let's talk money in the bank.
$1 at 100% interest
multiple interest compounding
f(x)=P(1+r/n)^(nt)
every minute every second
f(x)=Pe^rt
Three possible formulas, all tied closely together.
we can solve for anything...
as long as we estimate for anything that in the exponent.
3 example problems
7x=1
6x^2=3
100(1.02)^6=140
powers of 2
rewriting exponential functions as logarithms
a logarithm is the exponent that we do not know!
solving those logarithms
link to paper we talked about a little in class: http://hplengr.engr.wisc.edu/Math_Schoenfeld.pdf
If you go into a supermarket, you will typically see a number of checkout
counters, one of which is labeled "Express Lane" for x packages or fewer. If you
make observations on x, you'll find it varies a good deal. In my home town, the
A&P allow 6 items; the Shop-Rite, 8; and Kings, 10. I've seen numbers vary from
5 to 15 across the country. If the numbers vary that much, then we obviously
don't understand what the correct number should be. How many packages
should be allowed in an express line? (Pollak, 1987, pp. 260-261)