The scientific issue of carbon-14 dating and exponential decay gets a statistics-based treatment in this problem. The class starts with a basic investigation of carbon content, but then branches out to questions of accuracy and ranges of values. A great science-meets-math activity, where the context of the problem changes how the answer gets reported.

Concepts

carbon dating, estimation, exponential decay, inverse operations

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Additional Tags

math

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Instructional Ideas

• Link with a science unit on carbon dating of fossils or other prehistoric things
• Use as a review or application problem for inverse function pairs like exponential and log functions
• If the class has studied basic statistics, evaluate the error ranges in terms of standard deviations and p-values

Classroom Considerations

• Another method to solve Part b involves starting at a functional value of 10/2 = 5 and solving for t in terms of c. This might be more intuitive to pupils uncomfortable with inverse functions
• Learners without a strong physical science or statistics background might need more detailed explanation of giving a measured value as a range instead of a single value

Pros

• Real-life science application with numbers of actual magnitude and accuracy
• Provides opportunity for synthesis of inverse functions, interpretation of exponential decay, and developing meaningful answers in context

Cons

• Class worksheet not separated from teaching notes and answer key

Common Core

HSN-Q.A.3 HSF-LE.A.4