U7 L6 Exponential Growth and Decay completed.notebook
April 10, 2015
Unit 7: Exponential Functions
Lesson 6: Exponential Growth & Decay
RECALL:
Last class we compared linear, quadra c and exponen al func ons.
Success Criteria:
A er last class you should be able to...
iden fy whether a func on is linear, quadra c or exponen al from its
table of values, graph and equa on.
TODAY:
Success Criteria:
At the end of today's lesson, can you...
use the informa on given to come up with the equa on that models
real world exponen al growth and decay problems?
solve problems involving real world applica on of exponen al decay
and growth?
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U7 L6 Exponential Growth and Decay completed.notebook
April 10, 2015
RECALL: Exponen al func ons are func ons in the form
where
and
Exponen al func ons are o en used in the real-world to help describe the
growth and decay of popula ons, investments, etc.
NOTE:
It cannot always be used long-term. This becomes par cularly
evident with models of popula on growth as eventually the
popula on would become unsustainable.
KEY CONCEPTS:
Exponen al growth... is modeled by an increasing exponen al func on
(i.e. b > 1)
Exponen al decay...
is modeled by a decreasing exponen al func on
(i.e. 0 < b < 1)
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U7 L6 Exponential Growth and Decay completed.notebook
April 10, 2015
How to use the equa on y = a(b)x to model exponen al growth & decay:
y = the total (popula on/investment amount/etc.)
***NOTE: O en we use the variable 'P' instead of y when represen ng popula on
a = the ini al/star ng amount
***(think ABCs...a starts it off)
b = the growth rate
***(b > 1 for growth and 0 < b < 1 for decay)
For exponen al growth: b = 1 + r
For exponen al decay:
the rate
, where r is ___________
b= 1-r
x = number of growth/decaying periods (days/weeks/years/etc.)
***NOTE: O en we use the variables 'n' instead of x when represen ng popula on
For word problems...
STEP 1:
Find the important informa on (usually numbers).
Some key words to keep an eye out for...
* half-life:
this means that the b is _________
* doubles:
this means that the b is _________
* triples:
this means that the b is _________
* depreciates: this means that the b must be _________
STEP 2:
Take what you know and sub it into the equa on.
STEP 3:
Solve for what's missing.
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U7 L6 Exponential Growth and Decay completed.notebook
April 10, 2015
EX. 1. A bacteria colony has an ini al popula on of 200. The popula on
increases by 20% each day.
a) How many bacteria will there be in one week?
P=
a=
b=
t=
b) When will the popula on reach 2500?
P=
a=
b=
t=
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U7 L6 Exponential Growth and Decay completed.notebook
April 10, 2015
EX. 2. It is es mated that a new car depreciates by 20% per year.
a) Determine the value of a car a er 4 years if it costs $27,000 new.
P=
a=
b=
t=
b) When will the car be worth $8,000?
P=
a=
b=
t=
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U7 L6 Exponential Growth and Decay completed.notebook
April 10, 2015
EX. 3. Water lilies in a pond double each day. It takes 30 days for the lilies
to completely cover the pond. On what day was the pond half full of
water lilies?
P=
a=
b=
t=
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U7 L6 Exponential Growth and Decay completed.notebook
April 10, 2015
EX. 4. The remaining mass of a drug in a person's bloodstream is modelled
by
, where M is the remaining mass in milligrams,
and t is the me, in hours, that the drug is in the bloodstream.
a) What is the half-life of the drug?
b) What was the dosage of the drug?
c) What will be the concentra on of the drug in the bloodstream
i. a er 2 hours?
ii. a er 6 hours?
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U7 L6 Exponential Growth and Decay completed.notebook
April 10, 2015
Practice: p. 429 #2, 4, 7, 10
p. 437 #1, 3, 8, 9
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