Workshop on Geometry Software
Math 241
Spring 2015
Professor: Mike O'Sullivan
Week 5: Exponential Functions
First Day: Exponential functions and carbon dating
Let f(x)= 2^x.
We started the day by comparing the functions
g(x)= f(xp),
h(x)= f(x)+q,
k(x)= f(a*x),
m(x)= c*f(x),
and exploring how different values of
p, q, c, a affect the graphs of the corresponding functions.
We then saw that the m(x) functions can also be
represented in the form used in g(x), using rules of
exponents. Furthermore a function like k(x) can also be
expressed as an exponential with a different base.
Finally, we considered the mathematics behind carbon dating,
and how exponential functions play a role. The assumption in carbon
dating (in its rough form) is that when a living being dies, the
proportion of Carbon14 is the same as that in the atmosphere (which
we assume is the same as in today's atmosphere).
After that point, the the Carbon14 decays with halflife about 5730
years,
and the other forms of Carbon are stable.
Consequently, the proportion of Carbon14 in a dead being
declines over time.
This proportion can be used to infer the time since death.
Assignment:

Make a worksheet in which you present the following toy carbondating
problem.
On planet Frisbee, the proportion of Carbon14 is 10% of the total
carbon in the atmosphere and the rest is Carbon12.
An initial sample has 10,000 atoms of carbon.
Assume carbon has a halflife of 6000 years (it is fairly close to that
amount).
Give the formula for the total amount of carbon in the sample as a
function of time. Illustrate how one would use a measurement of the
amount of the carbon in the sample (many years later) to figure out
how much time has elapsed since the sample was created.
Pretend you have discussed exponential functions with your class and
explain how the graph relates to finding the age of the object.
Second Day: You will have time to work on all your projects.
Final Assignment:
 Create a GeoGebra book with chapters for the topics we have covered.
(Including the one above.)
Make corrections to your previous worksheets and polish the spelling,
grammar and presentation. Make good use of color and layout.
Upload your GeoGebra book.
Choose "Share with link" and send me the link via email.
(mosullivan@mail.sdsu.edu)
Due: Tuesday 3/24 at 5:00 pm.