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EXPONENTIAL FUNCTION
Math 12
ENRICHING MATHEMATICS INSTRUCTION
• Real life Math
BIG IDEA – ENTRY QUESTIONS
What does “Exponential” mean?
GROUP ACTIVITY What examples of local and global “Exponential Growth”
do you know?
Here are a few other things that grow exponentially:
• World population
• Oil consumption / Energy usage
• Global water consumption
• Debt
• Species extinction
• Global warming
• Growth of atmospheric carbon dioxide
THINK GLOBALLY, ACT LOCALLY
If your answer is yes!
Should we really care about all the exponential changes which are happening all around us?
Why? How?
LETS LOOK AT AN EXAMPLE:
Growth of World Population
WORLD POPULATION: “The rapid increase in human population over the
course of the 20th century has raised concerns
about whether Earth is experiencing overpopulation.
The scientific consensus is that the current
population expansion and accompanying increase in
usage of resources are linked to threats to the
ecosystem, such as rising levels of atmospheric
carbon dioxide, global warming, and pollution.”
(http://en.wikipedia.org/wiki/Population_growth)
WHERE DID DIFFERENT EXPONENTIAL EQUATIONS COME FROM?
In some applications of exponential functions, there is an underlying principle from which the equation is derived.
In other applications, the equation is found using empirical data. The equations are determined by calculating the equation of the exponential curve of best fit.
GROWTH OF BRITISH COLUMBIA ‘S POPULATION:
BRITISH COLUMBIA'S POPULATION GROWTH
trace to estimate the population in 2011
Trace to estimate when the population might reach 6 million
what are the effects of a growing population in British Columbia:
An Example:Increased
pressure on water resources
TAKE ACTION ! Living Water Smart - to keep our
water healthy and secure for the future
http://www.livingwatersmart.ca
THE RICHTER SCALE: comparing the
intensities of earthquakes
SOME EARTHQUAKES IN BC
Date Place Magnitude
June 23,1946 Near Campbell River
7.3
Aug22, 1949
Queen Charlotte Islands
8.1
June 24, 1997
SouthWesternBC
4.6
How many times as intense was: The 1964 earthquake compared to the
1997? The 1949 earthquake as the 1997
earthquake? The 1949 earthquake as the 1946
earthquake?
TAKE ACTION! Why do
earthquakes occur along the Canada’s west coast?
http://watch.ctv.ca/news/news/clip307624#clip307624
How can you become prepared for the next earthquake?
RADIOACTIVE DECAY
Chernobyl (April 1986)
Iodine-131 (half-life of 8.1 days)
Caesium-137 (half-life of 30 years).
Understanding exponential functions helps us understand phenomena in our environment
For example, population growth leads to an increase in pollution, and extra pressure on resources – we need to start planning for these things now, and having an understanding of what the population will be in the future is essential for that
“The greatest shortcoming of the human race is the inability to understand the exponential function.” Dr. Bartlett, professor of Physics.
REFERENCES:
http://www.coexist.es/en/exponential-growth.html
Wikipedia
Math 12 Text book
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