Solving Exponential and Logarithmic Equations
Solving Exponential and Logarithmic Equations
Objectives
In this lesson, students will write and solve exponential and logarithmic equations. Students will: [IS.2 - Struggling Learners]
- convert to and from exponential and logarithmic form.
- use the change of base formulas with the common logarithm and natural logarithm.
- solve real-world application problems using exponential and logarithmic equations.
- identify the domain and range of exponential and logarithmic functions.
- identify characteristics of the graphs of exponential and logarithmic functions.
- translate from one representation of an exponential or logarithmic function to another representation.
- identify what happens to the graph of an exponential or logarithmic function when the parameters change.
Essential Questions
How are relationships represented mathematically?
How can data be organized and represented to provide insight into the relationship between quantities?
How can expressions, equations, and inequalities be used to quantify, solve, model, and/or analyze mathematical situations?
How can mathematics support effective communication?
How can patterns be used to describe relationships in mathematical situations?
How can probability and data analysis be used to make predictions?
How can recognizing repetition or regularity assist in solving problems more efficiently?
How does the type of data influence the choice of display?
How is mathematics used to quantify, compare, represent, and model numbers?
What makes a tool and/or strategy appropriate for a given task?
- How can we determine if a real-world situation should be represented by a quadratic, polynomial, or exponential function?
- How do you explain the benefits of multiple methods of representing exponential functions (tables, graphs, equations, and contextual situations)?
Vocabulary
- Asymptote: A line such that a point, tracing a given curve and simultaneously receding to an infinite distance from the origin, approaches indefinitely near to the line; a line such that the perpendicular distance from a moving point on a curve to the line approaches zero as the point moves off an infinite distance from the origin. [IS.1 - Struggling Learners]
- Exponential Equation: An equation in the form of y=ax; an equation in which the unknown occurs in an exponent, for example, 9(x + 1) = 243.
- Logarithmic Equation: An equation in the form of y=logax, where x=ay; the inverse of an exponential equation.
- Domain: The set of all x-values or input values for an equation.
- Range: The set of all y-values or output values for an equation.
- Common Logarithm: Logarithm with base 10; if a = 10x, then log a = x.
- Natural Logarithm: Logarithm with base e; also ln, Napierian logarithm, Euler logarithm. The base, e, is approximately 2.71828.
Duration
120–180 minutes/2–3 class periods [IS.3 - All Students]
Prerequisite Skills
Prerequisite Skills haven't been entered into the lesson plan.
Materials
- Solving Exponential and Logarithmic Applications Worksheet (M-A2-4-2_Solving Exponential and Logarithmic Applications Worksheet.docx)
- Lesson 2 Exit Ticket (M-A2-4-2_ Lesson 2 Exit Ticket.docx)
- Graphing Exponential and Logarithmic Function Notes (M-A2-4-2_Graphing Exponential and Logarithmic Function Notes and KEY.docx)
- Graphing Practice Worksheet (M-A2-4-2_Graphing Practice Worksheet.docx)
- graph paper
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Formative Assessment
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DRAFT 11/05/2010