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