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Mathematics 12
Chapter 4
Modelling
1) At a seaport the depth of the water on a certain day is given by
2 (t 5)
d (t ) = 1.2 sin
+ 2.6 , where t is the hour in the day.
12.4
a) Amplitude:
Phase Shift:
Period:
Vertical Displacement:
b) When is the fi
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Modeling Using exponential functions
1) A population of bugs triples every 4 months. If the population starts at 300
bugs, then find the following:
a) How many bugs will there be in 9 months?
b) How many bugs will there be in 3 years?
c) When will
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4
For the equation y = 3 sin 2 x
+ 2 , determine the following: (exact values)
3
Amplitude:
(1/2 mark)
Phase shift:
(1/2 mark)
Period:
(1/2 mark)
Vertical displacement:
(1/2 mark)
Minimum:
(1/2 mark)
Maximum:
(1/2 mark)
Where the first minimum
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If A =
B2
and log B = 4 , log C = 3 , and log D = 5 , find the value of log A .
C 3D
Simplify the following:
x log 2 12 x log 2 80
A)
x log 2 120
B) 2 log x 6 + log x 18 + log x 54
C) log x a 2 y 3 log x a 4 y 5 + log x a y +1
If A =
B3
and log B = 3 , lo