Introduction
Exponential growth
is a process that occurs all around us in real life. If you put money
in a bank account, it grows exponentially. Cancer cells grow exponentialy.
The population of the world grows exponentially. Anything that
grows at a fixed percent is growing exponentially.
Standards
Addressed
Algebra 1 Standards
-
Standard 2 - Students
understand and use rules of exponents
-
Standard 15 - Students
use Algebraic techniques to solve rate problems
-
Standard 17 - Students
determine the domain of independent variables and the range of dependent
variables defined by a graph, set of ordered pairs or a symbolic expression.
Instructional
Objectives
Students Will
Be Able To:
1.
Give examples of things that grow exponentially
2.
Explain the difference between linear growth and exponential growth.
3.
Graph the growth of a population given the starting population and rate
of growth.
4.
Calculate the population after a specified amount of time.
5.
Calculate the amount of time needed for a population to reach a certain
number.
6.
Explain how this relates to the amount of money you can make if you invest
wisely.
Student
Activities
Students begin day
one with the following question:
You have just
won the grand prize on a game show. The game show host tells you
that you may choose from one of two cash prizes but you only have 30 seconds
to decide. Your choices are
$1,000 per day
for 30 days
$0.01 (one penny)
the first day, $0.02 the next
day, $0.04 the
next day....for 30 days. Each day's pay is
double the pay
from the previous day.
Which would you
choose?
Most students
will choose Prize #1. Ask them to calculate
the total money
for each prize on a sheet of paper and
they will realize
that they would be multimillionaires if
they chose prize
2. After students have calculated the
prize amounts
they will graph both amounts on seperate
graphs.
This is the power of exponential growth.
This activity
can also be extended to find the formula for exponential growth by using
the student's calculations of the prize money and searching for the pattern.
Once students notice a patter they can generalize the pattern for all cases.
They have now discovered the formula for exponential growth.
Assessment
Rubric for Introductory
Activity
5 points
-
Prize amounts have been accurately
calculated for the entire 30 day period
-
Prize amounts have been accurately
graphed on seprate graphs
-
Graphs are neat and clearly labeled
-
Student has explained the differences
that he/she noticed between the two graphs
4 Points
-
Prize amounts have been accurately
calculated for the entire 30 day period
-
Prize amounts have been accurately
graphed on seprate graphs
-
Graphs are neat but not labeled
-
Student has explained the differences
that he/she noticed between the two graphs
3 Points
-
Prize amounts have been accurately
calculated for the entire 30 day period
-
Prize amounts have been accurately
graphed on seprate graphs
-
Graphs are poorly drawn and not
labeled
-
Student has not clearly explained
the differences that he/she noticed between the two graphs
2 Points
-
Prize amounts have been accurately
calculated for the entire 30 day period
-
Prize amounts have not been graphed
Results
Due to
the fact that this page was created in the middle of the summer this lesson
has yet to be fully implemented and as such there are no results.
However, you may be sure that as soon as I try this lesson with my students
I will post the results here ASAP. Thanks for your patience.
Web
Resources & Supplementary Materials
Here is
a list of some sites that I have found which provide additional informattion
about exponential growth as well as problems for your classroom.
http://www.cs.utah.edu/~zachary/computing/lessons/uces-4/uces-4/uces-4.html
This is
an an excellent resource with examples of growth relating to bank accounts.
This lesson also requires students to use inductive reasoning to determine
the pattern for the amount of money after x years.
http://math.usask.ca/readin/examples/expgrtheg.html
This site
contains examples using logarithms to model exponential growth.
http://zebu.uoregon.edu/1997/ph161/l6.html
This site
is very useful. It expalins how a lack of understanding about exponnential
growth can lead to disaster when planning the use of resources. Growth
is good, but too much growth and we may run out of water or other resources
which are essential for human survival.
http://www.utm.edu/~rirwin/expgrowth.htm
This has
a growth table with iterations. Just enter starting population and
growth rate and it will run 100 iterations. I didn't list this on
the student site because it can be used as a shortcut to many of my activities.
Works great as supplementary tool for class lectures.
http://cauchy.math.colostate.edu/Applets/ExponentialGrowth/exponentialgrowth.htm
Cool graph.
This graph is really cool. You can play around with the initial condition
and growth rate and watch the graph change.
http://www.jump.net/~otherwise/population/exponent.html
Virtual
pond. This virtual pond allows the students to watch the population
of fish in a virtual pond exceed the limits of their environment(the computer
screen).
Make sure to check out my student
website.
Packed with activities, projects and best of
all cool links!
...And it's more flashy than this page.
What's the best book of all time? Click
here to find out.
Created by Anthony Kudsi
Independence
High School
1776 Educational
Park Drive, San Jose CA
Last Revised:
7/25/2000 |
Bill
says,"This
page is the ultimate resource for understanding the effects of exponential
growth and decay." 
