Transcript + Exponential Equations
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Exponential Equations M2 Unit 5a: Day 8 EQ: How do we solve exponential equations & inequalities algebraically a n d g r a p h i c a l l y ?
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1.
Quiz over Unit 5A Days 4-6 Graph the following function:
y
1 2
x
зи ш + 3 2.
Is the function an exponential growth or decay function?
3.
4.
5.
6.
7.
8.
Describe the translation Find the asymptote Find the domain Find the range Describe the end behavior: As
x
® Ґ ® __ and as x ® __ You deposit $1200 in an account that pays 8% annual interest. Find the balance after 2 years is compounded annually.
A
P
1
r n
nt
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Vocabulary Exponential equation – an equation in which variable expressions occur as exponents Solve by equating exponents Find a common base Set the exponents equal to each other Solve for the variable
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Watch me as I work one… Solve by equating exponents
125
x
3
(5 )
x
25
x
1 2
(5 )
x
1
5
3
x
3
x x
5
2
x
2
2
x
2 2
Rewrite powers with base 5 Simplify the exponents Drop the bases and set the exponents = Solve for
x
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Solve by equating exponents
1. 2
x
6
4
x
4
2. 64
16
x
1
x
1 2
3. 5
3
x
1
25
x
1
x
1
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Multiple choice. Find the solution.
4. 2
x
7 16
x
2 5. 9 2
x
3
x
6
9
3
1
4
5
5
6
2
6
2
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What if you have a fraction in the equation?
x
1
6.
2
2
x
7. 3
x x
3
x
1 2
x
2
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What is the answer if you have an equation like this?
8. 1
x
1
x
1 The answer is All real numbers, because any x-value can be plugged in to make a true statement.
9. 5
3
x
5
3
x
All real numbers
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To Solve by Graphing: The solution is the x value of the intersection point Look back at problems 6 and 7. What is the solution?
6. 1
x
1 2 2
x
7. 3
x
1
x
3
x
= 0.5
x
= 2
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To solve exponential inequalities algebraically: •Find a common base •Write an inequality using the exponents •Solve for the variable
1. 4
3
x
8
x
1
2. 3
4
x
9
x
3
x
1
x
3
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Solve exponential inequalities algebraically
3. 8
x
2
2
x
1
4. 4
2
x
5
64
3
x x
1
x
5 7
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Multiple choice. 11
x
5. 36
5
x
2
2
5
5
3
3 3 2
6. 3
3
x
7
81
9
19
6
11 3
9
x
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Homework pg 130 # 2-8 even, 10 – 15 all, 19, 20