standard_description: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
problem_activity: Task
The half-life of Carbon $14$, that is, the time required for half of the Carbon $14$ in a sample to decay, is variable: not every Carbon $14$ specimen has exactly the same half life. The half-life for Carbon $14$ has a distribution that is approximately normal with a standard deviation of $40$ years. This explains why the Wikipedia article on Carbon $14$ lists the half-life of Carbon 14 as $5730 \pm 40$ years. Other resources report this half-life as the absolute amounts of $5730$ years, or sometimes simply $5700$ years.
Explain the meaning of these three quantities ($5730 \pm 40$, $5730$, and $5700$) focusing on how they differ.
Can all three of the reported half-lives for Carbon $14$ be correct? Explain.
What are some of the benefits and drawbacks for each of the three ways of describing the half-life of Carbon $14$?


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