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CMIC 2/3
Unit 5
Warm Up
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The operating cost of a store that sells only ipods
can be modeled as a function of the number of
ipods that the store purchases from the supplier.
The rule for that function is:
C(x) = 3500 + 35x
Evaluate and explain the meaning of:
C(5)
C(20)
C(x) = 4095
S(x)=4000 – 250x
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Evaluate S(10)
S(x)=4000 – 250x
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Evaluate S(10)
S(10) = 4000 – 250(10)
S(10) = 1500
S(x)=4000 – 250x
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Evaluate S(x) = 1000
S(x)=4000 – 250x
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Evaluate S(x) = 1000
1000 = 4000 – 250x
-4000 -4000
-3000 = -250x
-250
-250
12 = x
Rewrite in Standard Form
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(x + 5)(x – 2)
Rewrite in Standard Form
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(x + 5)(x – 2)
x2 – 2x + 5x – 10
x2 + 3x – 10
Factor the following
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x2 + 8x – 20
Factor the following
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x2 + 8x – 20
-20
-2
10
8
 (x + 10)(x – 2)
Find the x-intercept (zeros)
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x2 + 8x + 15
Find the x-intercept (zeros)
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x2 + 8x + 15
15
5
3
8
 (x + 5)(x + 3)
x + 5 = 0

x = -5
x+3=0
x = -3
Find the vertex (minimum or maximum
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x2 + 8x + 15
Find the vertex (minimum or maximum
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x2 + 8x + 15
a=1
b=8
c = 15
-b/2a = -8/2 = -4
(-4)2 + 8(-4) + 15 = -1
vertex = (-4, -1)
Find the y-intercept and Graph
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x2 + 8x + 15
Find the y-intercept and Graph
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x2 + 8x + 15
y- int = 15
Solve using the quadratic formula
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3x2 – 10x + 7 =0
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6x2 + 7x – 10 = -5
Common Logs …
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Calculate the following:
log 1000
log 0.001
log 78
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Explain why the answer makes sense
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Problem 1
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Solve the following:
log 1000
Problem 1
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Solve the following:
log 1000 = 3
Problem 2
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Solve the following:
log 0.001
Problem 2
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Solve the following:
log 0.001= -3
Problem 3
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Solve the following:
log -71
Problem 3
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Solve the following:
log -71= no solution
Problem 4
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Explain why the following statement is true:
log 100 = 2
Problem 4
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Explain why the following statement is true:
log 100 = 2
It is true because 102 = 100.
Problem 5
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Explain why the following statement is true:
1 < log 65 < 2
Problem 5
Explain why the following statement is true:
1 < log 65 < 2
It is true because 65 is between 10(101) and
100 (102).
This is true because the log of 65 is 1.812
which is between the numbers 1 and 2.
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Problem 6
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Explain why the following statement is true:
log 0.1 = -1
Problem 6
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Explain why the following statement is true:
log 0.1 = -1
It is true because 10-1 = 0.1.
Problem 7
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Solve the following equation:
10x = 45
Problem 7
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Solve the following equation:
10x = 45
log 10x = log 45
x = 1.653
Problem 8
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Solve the following equation:
104x = 0.457
Problem 8
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Solve the following equation:
104x = 0.457
log 104x = log 0.457
4x = -.34
4
4
x = -.085
Problem 9
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Solve the following equation:
10x+3 = 6730
Problem 9
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Solve the following equation:
10x+3 = 6730
log 10x+3 = log 6730
x + 3 = 3.828
-3
-3
x = 0.828
Problem 10
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Solve the following equation:
6(102x )= 600
Problem 10
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Solve the following equation:
6(102x )= 600
102x = 100
log 102x = log100
2x = 2
x=1
Problem 11
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Complete the table:
x
0.5
1
5
10
log(x)
Problem 11
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Complete the table:
x
log(x)
0.5
-0.3
1
0
5
0.699
10
1
Warm Up
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Solve each equation:
 10x
= 63
 104x = 320
 10x+2 = 2700
 (Hint:
Use logarithms to help solve)
Warm Up
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Solve each equation:
 10x
= 68
 103x = 0.587
 10x+2 = 7820
 (Hint:
Use logarithms to help solve)
#8 p.385
#9 p.385