SECT. 2.4 MODELLINGSITUATIONS WITH EXPONENTIALFUNCTIONS
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I) APPLICATIONS OF EXPONENTIAL FUNCTIONS
Exponential Functions have many different applications
Nature:
Population Growth, Earthquakes (Ritcher Scale)
Radio active Decay
Science: (Chemical, Biological, Physical)
PH levels (Acid & Bases),
Bacteria Growth (Colonies)
Sound Intensities (Decibels), Light Intensities,
Finances:
Amortizations, Mortgages, Investments, Interests
Depreciation/Appreciation
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II) TERMS & FINAL EQUATION:
Double Time: The time it takes a population or theweight of an object to double its size or value
Half – Life: The time it takes a population or object todepreciate to half its size or value
Ie: Time it takes a
population to double
Ie: Time required to
reach Half - Life
Annually: L = 1
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EX: COCKROACH QUESTION:
If a colony of 2 cockroaches doubles everyday, how many cockroaches will there beafter 1 week?
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Ex: If a colony of 12 cockroaches doubles every 3days, after how many days will the population beover 10,000?
After 30 days, the populationof the cockroaches will beover 10,000!!
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II) HOW DOES RADIOCARBON DATING METHODS WORK?
There are two types of carbon in our bodies C12 & C14
Carbon intakes occur through eating plants plantsobtain carbon through atmosphere
C12 – Stable isotope of carbon
C14 – Unstable, decays (Radioactive) (2 extra neutrons)
Living tissues have equal amounts of both carbon
When an organism dies, carbon intake ceases and theratio of C12 to C14 is locked.
Ratios of C12 to C14 are measured to calculate the age
Method of calculating age (3 step process)
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Ex: The half life of C-14 is 5730 years. How long will ittake 820g of C-14 to decay to 13g?
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Practice) A radio active substance decays 20% in 120years. What is the half life of the substance?
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HOMEWORK:
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