Understand the concepts of logarithmic and exponential functions. Graph exponential functions, and solve problems of growth and decay. Understand the inverse relationship between exponents and logarithms, and use it to prove laws of logarithms and to solve equations. Convert logarithms between bases, and simplify logarithmic expressions.
Number: MA.912.A.8
Title: Logarithmic and Exponential Functions
Type:
Standard
Subject: X-Mathematics (former standards - 2008) - Archived
Grade: 912
Body of Knowledge: Algebra
Related Benchmarks
This cluster includes the following benchmarks
| Code |
Description |
| MA.912.A.8.1: | Define exponential and logarithmic functions and determine their relationship |
| MA.912.A.8.2: | Define and use the properties of logarithms to simplify logarithmic expressions and to find their approximate values. |
| MA.912.A.8.3: | Graph exponential and logarithmic functions. |
| MA.912.A.8.4: | Prove laws of logarithms. |
| MA.912.A.8.5: | Solve logarithmic and exponential equations. |
| MA.912.A.8.6: | Use the change of base formula. |
| MA.912.A.8.7: | Solve applications of exponential growth and decay. |
Related Resources
Vetted resources educators can use to teach the concepts and skills in this topic.
Problem-Solving Tasks
| Name |
Description |
| Ponzi Scheme Pondering: | The students must rationalize how a Ponzi email could make money or fall apart. Using their knowledge of exponential growth, the students can estimate the potential gains, but then are asked to think about why these schemes are illegal and tend to collapse. |
| Get a Half-life!: | In this activity students are challenged to model a decay function by collecting data from a few trials, graphing the data, and then drawing a curve of best fit. The student must decide which of the equations best fits his/her data. |
Video/Audio/Animation
| Name |
Description |
| MIT BLOSSOMS - Flu Math Games: | This video lesson shows students that math can play a role in understanding how an infectious disease spreads and how it can be controlled. During this lesson, students will see and use both deterministic and probabilistic models and will learn by doing through role-playing exercises. There are no formal prerequisites, as students in any high school or even middle school math class could enjoy this learning video. But more advanced classes can go into the optional applied probability modeling that accompanies the module in a downloadable pdf file. The primary exercises between video segments of this lesson are class-intensive simulation games in which members of the class 'infect' each other under alternative math modeling assumptions about disease progression. Also there is an occasional class discussion and local discussion with nearby classmates. |
