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Finding Equations of Exponential Function Section 4.4

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Lehmann, Intermediate Algebra, 4ed Section 4.4 An exponential curve contains the points listed in the table. Find an equation of the curve. Slide 2 Finding an Equation of an Exponential Curve Using the Base Multiplier Property to Find Exponential Functions Example Solution Exponential is of the form f(x) = ab x y-intercept is (0, 3), so a = 3 Input increases by 1, output multiplies by 2: b = 2 f(x) = 3(2) x

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Lehmann, Intermediate Algebra, 4ed Section 4.4 Verify results using graphing calculator Slide 3 Finding an Equation of an Exponential Curve Using the Base Multiplier Property to Find Exponential Functions Solution Continued

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Lehmann, Intermediate Algebra, 4ed Section Find a possible equation of a function whose input – output pairs are listed in the table. Slide 4 Linear versus Exponential Functions Using the Base Multiplier Property to Find Exponential Functions Example Solution x increases by 1, y multiplies by 1/3: b = 1/3 y-intercept is (0, 162): a = 162.

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Lehmann, Intermediate Algebra, 4ed Section Find a possible equation of a function whose input – output pairs are listed in the table. Slide 5 Linear versus Exponential Functions Using the Base Multiplier Property to Find Exponential Functions Example Solution x increases by 1, y subtracted by 4: Linear function y-intercept is (0, 50) y = 4x + 50

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Lehmann, Intermediate Algebra, 4ed Section 4.4 Find all real-number solutions. Slide 6 Linear versus Exponential Functions Solving Equations of the Form ab n = k for b Example Solution 1. Solutions are 5 and –5 Use the notation 5

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Lehmann, Intermediate Algebra, 4ed Section Check that both –2 and 2 satisfy the equation. Slide 7 Linear versus Exponential Functions Solving Equations of the Form ab n = k for b Solution

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Lehmann, Intermediate Algebra, 4ed Section Check that 1.55 approx. satisfies the equation. 5.The equation b 6 = –28 has no real solution, since an even exponent gives a positive number. Slide 8 Linear versus Exponential Functions Solving Equations of the Form ab n = k for b Solution

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Lehmann, Intermediate Algebra, 4ed Section 4.4 To solve an equation of the form b n = k for b, 1.If n is odd, the real-number solution is 2.If n is even, and k ≥ 0, the real-number solutions are. 3.If n is even and k < 0, there is no real number solution. Slide 9 Solving Equations of the Form b n = k for b Solving Equations of the Form ab n = k for b Summary

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Lehmann, Intermediate Algebra, 4ed Section 4.4 Find all real-number solutions. Round your answer to the second decimal place b 6 – 3.19 = Slide 10 One-Variable Equations Involving Exponents Solving Equations of the Form ab n = k for b Example Solution

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Lehmann, Intermediate Algebra, 4ed Section Slide 11 One-Variable Equations Involving Exponents Solving Equations of the Form ab n = k for b Solution Continued

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Lehmann, Intermediate Algebra, 4ed Section 4.4 Find an approximate equation y = ab x of the exponential curve that contains the points (0, 3) and (4, 70). Round the value of b to two decimal places. y-intercept is (0, 3): y = 3b x Substitute (4, 70) and solve for b Slide 12 Finding Equations of an Exponential Function Using Two Points to Find Equations of Exponential Function Example Solution

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Lehmann, Intermediate Algebra, 4ed Section 4.4 Our equation is y = 3(2.20) x Graph contains (0, 3) b is rounded Doesn’t go through (0, 70), but it’s close Slide 13 Finding Equations of an Exponential Function Using Two Points to Find Equations of Exponential Function Solution Continued

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