Grade 11 University: (MCR3U) Unit 3: Exponential Functions Solving Exponential Equations 1 Mr. Choi © 2018 E. Choi – MCR3U - All Rights Reserved.

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Grade 11 University: (MCR3U) Unit 3: Exponential Functions Solving Exponential Equations 1 Mr. Choi © 2018 E. Choi – MCR3U - All Rights Reserved

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 © 2018 E. Choi – MCR3U - All Rights Reserved

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 © 2018 E. Choi – MCR3U - All Rights Reserved

B: Solving Exponential Equations by Graphing © 2018 E. Choi – MCR3U - All Rights Reserved

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 © 2018 E. Choi – MCR3U - All Rights Reserved

Example 1: Solving Exponential Equations Algebraically (B.A.T.S.) © 2018 E. Choi – MCR3U - All Rights Reserved

Example 3: Solving Exponential Equations Algebraically (B.A.T.S.) © 2018 E. Choi – MCR3U - All Rights Reserved

Example 5: Solving Exponential Equations Algebraically (B.A.T.S.) Method 2 Solving Exponential Equations 1 © 2018 E. Choi – MCR3U - All Rights Reserved

Example 6: Solving Exponential Equations Algebraically (B.A.T.S.) © 2018 E. Choi – MCR3U - All Rights Reserved

Example 7: Solving Exponential Equations Algebraically (B.A.T.S.) Method 2: Method 3: Solving Exponential Equations 1 © 2018 E. Choi – MCR3U - All Rights Reserved

Example 8: Solving Exponential Equations Algebraically (B.A.T.S.) © 2018 E. Choi – MCR3U - All Rights Reserved

Homework Work sheet: Solving Exponential Equations 1 Text: Check the website for updates Solving Exponential Equations 1 © 2018 E. Choi – MCR3U - All Rights Reserved

End of lesson Solving Exponential Equations 1 © 2018 E. Choi – MCR3U - All Rights Reserved