Workshop on Geometry Software
Professor: Mike O'Sullivan
Week 5: Exponential Functions
Here is a summary of what we did on Tuesday Oct 12, with details on the assignment.
Week 4 Exponential
First Day: Exponential functions and carbon dating
Let f(x)= 2^x.
We started the day by comparing the functions
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 Carbon-14 is the same as that in the atmosphere (which
we assume is the same as in today's atmosphere).
After that point, the the Carbon-14 decays with half-life about 5730
and the other forms of Carbon are stable.
Consequently, the proportion of Carbon-14 in a dead being
declines over time.
This proportion can be used to infer the time since death.
Make a worksheet in which you present the following toy carbon-dating
On planet Frisbee, the proportion of Carbon-14 is 10% of the total
carbon in the atmosphere and the rest is Carbon-12.
An initial sample has 10,000 atoms of carbon.
Assume carbon has a half-life of 6000 years (it is fairly close to that
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.
Final Day: You will have time to work on all your projects.
Upload your GeoGebra book.
Choose "Share with link" and send me the link via email.
- 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.
Due: Halloween, at midnight.