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NEWS. Still pondering what to do with the test Quiz will be a TAKE-HOME (due Wednesday) Wednesday at lunch I will be going over the test (we have class right before). Free Powerpoint Templates. TAKE HOME QUIZ. Worksheet #1c ON WEBSITE if you lost it Worksheet #3 - PowerPoint PPT PresentationTRANSCRIPT
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NEWS• Still pondering what to do with the test• Quiz will be a TAKE-HOME (due Wednesday)
• Wednesday at lunch I will be going over the test (we have class right before)
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TAKE HOME QUIZ1. Worksheet #1c ON WEBSITE if you lost it
2. Worksheet #3
3. Workbook p.159 #2e4. Workbook p.160 #3d (SHOW YOUR WORK OR YOU GET ZERO!!)
5. Workbook p.174 #3b
6. Workbook p.176 #7e
7. Workbook p. 176 #8f
8. Workbook p. 177 #12b
9. Workbook p.177 #14c
10. Workbook p.179 #25b
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Let’s go over a log question…p. 177 #12a 4ln2x + ln(6/x) – 2ln2x
= ln(2x)4 + ln(6/x) – ln(2x)2
= ln16x4 + ln(6/x) – ln4x2
= ln(16x4∙6) x∙4x2
= ln(96x4) 4x3
= ln24x
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Solving Log EquationsExample 1
log(x+1) = 1 – log(x-2)Restrictions: x>-1 and x>2
log(x+1) + log(x-2) = 1log((x+1)(x-2)) = 1
(addition law)
101 = (x+1)(x-2)(change to exponential form)
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Solving Log EquationsExample 1
x2 – x – 2 = 10
x2 – x – 12 = 0(x+3)(x-4) = 0
(factoring)
x=-3 and x=4Because of the restrictions, we reject x=-3
S={4}
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Solving Log EquationsExample 2
ln(x+2) = ln(-x+6) + ln(x-1)Restrictions: x>-2, x<6, x>1
ln(x+2) = ln((-x+6)(x-1))(x+2) = (-x+6)(x-1)
(divide both sides by ln)
x+2 = -x2 + 7x - 6(expand)
-x >-6 x<6
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Solving Log EquationsExample 2
x2 – 6x + 8 = 0(x-2)(x-4) = 0
(factoring)
x=2 and x=4Both fit the restrictions
S={2,4}
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Growth & DecayIntro to Exponential Functions
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Formulas
GROWTH = (P)(1+interest rate)time
DECAY = (P)(1-interest rate)time
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Example 3How much money will you have if you invest
700$ at 7.5% compounded annually for 15 years?
f(x) = (700)(1.075)15
= $2071.21
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Example 4You buy a car for $25000. If it depreciates
by 4.3% annually, what’s the value of the car 10 years later?
f(x) = (25000)(1- 0.043)10
f(x) = (25000)(0.957)10
= $16108.66
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Example 5An investment of $600 at 8% grows to
$7280. For how long was it invested?
7280 = (600)(1.08)x
12.13 =(1.08)x
log1.0812.13 = x(change to log form)
x = (log12.13)/(log1.08) = 32.43
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Example 6An investment at 6% grows to $1296 in 12
years. What was the initial investment?
1296 = (P)(1.06)12
1296 =(P)(2.012)
$644.07 = P
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Example 7An investment of $900 grows to $1340 in 8
years. What rate of interest did the investment earn?
1340 = (900)(1+r)8
1.48 =(1+r)8
(1.48)1/8 =(1+r)8∙(1/8)
(to get rid of the exponent)
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Example 7An investment of $900 grows to $1340 in 8
years. What rate of interest did the investment earn?
1.051 = 1+r
0.051 = r
So 5.1%
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HOMEWORK• TAKE HOME QUIZ
• Workbook p.137 #3,4,5,6 p.180-181 #27, 28
• Worksheet Side 2 #1,2