# Use Exponential Models and Solve a Contextual Problem with Logarithms

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Students will use an exponential model for a contextual situation involving radioactive half-life. Each version uses a half-life model; N(t) = No 2^(-t/t1/2) where No is the initial amount, t is the time of decay and t1/2 is the half life of the isotope. There is also an additional question that uses the calculus derived, model in the form
N(t) =No e-rt, where r is the decay constant (r is usually represented with the Greek letter lambda).

The assignment requires students to use logs and graphing calculators to solve a contextual problem as well as interpret variables, domain and range as they pertain to a real life context.

The two forms of decay model allow students to see how common logs are used to solve problems as well as connect the concept of continuous decay/growth to a real life base e model. The base e model is also conveniently solved with a natural logarithm.

Notes:

In the base e model, r (the decay constant) is usually represented as lambda (no lambda key on the keyboard). Additionally, the decay constant has a unit called a Becquerel. Because a Becquerel is a unit of nuclear, it may be prudent to simply have students find numerical values for the decay constant without credence to its actual meaning. This way, students can still see how the base e function works without being required to do any half-life to Becquerel interpretations.

This is a ONE page assignment, but I have included FOUR different versions. Multiple versions might be used for academic integrity purposes, re-take opportunities, or group work.

This product is also available as part of a bundle in my store:
Logarithmic Functions: A Bundle of Activities and Assessments.

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Total Pages
4 pages
Not Included
Teaching Duration
30 minutes
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