1. Grade 11 University: (MCR3U) Unit 3: Exponential Functions Solving Exponential Equations 1
Mr. Choi
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2. Properties of the Exponential Function 𝒚= 𝒃 𝒙
The base b is positive.
The y-intercept = 1.
(3) The horizontal asymptote is the x-axis (i.e. y = 0)
(The graph does not touch the x-axis, but getting close to it.)
(4) The domain: x ∈ R.
(5) The range: y ∈ R, y > 0 (i.e. the H.A.)
(6) If b > 1, the exponential function is always increasing.
(7) If 0 < b < 1, the exponential function is always decreasing.
Key points: 𝑦= 𝑏 𝑥
Note:
The graphs y = bx and y = b-x are symmetrical about the y-axis.
Solving Exponential Equations 1
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3. A: Concept
Exponential expression: has no f(x) or equal sign in the expression
ie)
Exponential function: , the variable is the exponent
Exponential equations: have bases on both sides with no in the expression
ie) , ,
To solve an exponential equation means to determine the value of the unknown variable, the exponent.
Solving Exponential Equations 1
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4. B: Solving Exponential Equations by Graphing
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5. C: Solving Exponential Equations Algebraically (B.A.T.S.)
Bases Are The Same
Recall the power rule for exponents:
keep the base and multiply the exponents.
Rewrite both sides of the equation with a same base using
exponent rules. Only 1 base per side.
If necessary, simplify the exponents ie) follow power rule from the exponent laws.
Equate the exponents (means: create an equation using the
exponents only).
4. Solve for the variable. Check.
Solving Exponential Equations 1
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6. Example 1: Solving Exponential Equations Algebraically (B.A.T.S.)
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7. Example 3: Solving Exponential Equations Algebraically (B.A.T.S.)
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8. Example 5: Solving Exponential Equations Algebraically (B.A.T.S.)
Method 2
Solving Exponential Equations 1
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9. Example 6: Solving Exponential Equations Algebraically (B.A.T.S.)
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10. Example 7: Solving Exponential Equations Algebraically (B.A.T.S.)
Method 2:
Method 3:
Solving Exponential Equations 1
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11. Example 8: Solving Exponential Equations Algebraically (B.A.T.S.)
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12. Homework
Work sheet: Solving Exponential Equations 1 Text: Check the website for updates
Solving Exponential Equations 1
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13. End of lesson Solving Exponential Equations 1
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