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Understanding Exponential Functions and Half-Life in Radioactive Decay

Explore the concept of exponential functions, particularly focusing on half-life as a model for phenomena that decrease over time, such as radioactive decay. The half-life of a radioactive substance represents the time needed for half of it to decay to a non-radioactive state. For example, if a radioactive substance has a half-life of 14 days and starts with 6.6 grams, you can model the remaining quantity over time. This guide will explain how to express the amount remaining, calculate when only 1 gram will remain, and apply this knowledge through examples.

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Understanding Exponential Functions and Half-Life in Radioactive Decay

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  1. 1.3 Exponential Functions

  2. Exponential Function

  3. Rules for Exponents

  4. Half-life Exponential functions can also model phenomena that produce decrease over time, such as happens with radioactive decay. The half-life of a radioactive substance is the amount of time it takes for half of the substance to change from its original radioactive state to a non-radioactive state by emitting energy in the form of radiation.

  5. Exponential Growth and Exponential Decay

  6. Ex: The half-life of a certain radioactive substance is 14 days. There are 6.6 g present initially.A. Express the amount of substance remaining as a function of time t.B. When will there be 1g remaining?

  7. The Number e

  8. The Number e

  9. Do example 5 on page 25

  10. Hwk: p. 26, 1-19 (odd), 21-39 (mults of 3)

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