MA.912.A.8.7Archived Standard

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Solve applications of exponential growth and decay.

Remarks

Example: The population of a certain country can be modeled by the equation , where P(t) is the population in millions and t is the number of years after 1900. Find when the population is 100 million, 200 million, and 400 million. What do you notice about these time periods?
General Information
Subject Area: X-Mathematics (former standards - 2008)
Grade: 912
Body of Knowledge: Algebra
Idea: Level 3: Strategic Thinking & Complex Reasoning
Standard: Logarithmic and Exponential Functions - 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.
Date Adopted or Revised: 09/07
Content Complexity Rating: Level 3: Strategic Thinking & Complex Reasoning - More Information
Date of Last Rating: 06/07
Status: State Board Approved - Archived

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Problem-Solving Tasks

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.

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

Video/Audio/Animation

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.

Type: Video/Audio/Animation

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