EXPONENTIAL RELATIONS
(APPLICATIONS)
A. LINEAR vs. QUADRATIC vs. EXPONENTIAL RELATIONS
Complete each table and classify each relation:
y = 2x
x
–3
y = x2
y
y
x
–3
–2
–2
–1
–1
0
0
1
1
2
2
3
3
y
y
 2y
y = 2x
x
y
y
x
–3
–2
–1
0
1
2
3
Summary:
In a linear relation, ____________________ are constant.
In a quadratic relation, ____________________ are constant.
In an exponential relation, ____________________ are constant.
Unit 4 Lesson 4
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B.
APPLICATIONS of EXPONENTIAL RELATIONS
Example 
Sid the Science Kid studied a pond where frogs lay eggs. He found
that the number of tadpoles increased by a factor of 2.43 per day.
The number of tadpoles can be modelled by the equation,
T = 265(2.43)t, where T is the number of tadpoles and t is the time in
days.
a)
Determine the number of tadpoles initially present in the pond.
this is the
T–intercept
b)
Determine the number of tadpoles present after:
i)
3 days
ii)
1 week
In general, an exponential equation has the form:
A = Ao(r)t
Unit 4 Lesson 4
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Example 
Late in the summer, the blackfly population starts to decrease by 4%
per day. The population can be modelled by the equation,
P = 6720(0.96)t, where P is the population of blackflies and t is the
time in days.
a)
State the initial blackfly population.
b)
Determine the number of days it will take for the blackfly
population to be reduced to half of its original amount.
Homework: p.390–392 #1, 6bc, 7bc, 9
p.401 #1bcd, 2bc
Unit 4 Lesson 4
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