HONORS STUDENTS:
The following is a somewhat challenging video, that students need to approach with SERIOUS CONFIDENCE. What do I mean?
Student should take this video SERIOUSLY, because it uses concepts (and calculator functions) that are typically not encountered by most high school students until a third-year math course. Most of you are sophomores, and have not taken a third-year math course!
But, students should also approach this new material with CONFIDENCE, because it doesn't actually require you to have a deep understanding of the functions used in the calculations.
Instead, it focuses in a practical way on just using buttons on the calculator to set up and solve problems----and, as you know, we've been that the entire year! So, if you take it seriously and remember that you have already been expected to learn new calculator routines to solve problems, then this is nothing new---and nothing you can't handle!
The video begins with examining two functions found on a student's calculator: 'e^x' (a function of Euler's number) and 'LN' , natural logarithms ('ln' or 'natural log', for short).
It explains how these functions 'mirror' each other as they describe exponential processes.
Your instructor then shows how radioactive half-life (t^1/2) and decay constants (k) can be derived from each other by using them to divide the natural log of 2 (ln 2, or .693).
Finally, your instructor shows two related equations, one than employs natural log (ln), and one which employs 'e^x', to predict how samples of radioactive isotopes might change over time.
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