options: Reason quantitatively and use units to solve problems.

Use properties of rational and irrational numbers.

Apply and extend previous understandings of numbers to the system of rational numbers.

Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

Perform operations on matrices and use matrices in applications.

Compute fluently with multi-digit numbers and find common factors and multiples.

Extend the properties of exponents to rational exponents.

Perform operations on vectors.

Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

Represent and model with vector quantities.

Represent complex numbers and their operations on the complex plane.

Know that there are numbers that are not rational, and approximate them by rational numbers.

Perform arithmetic operations with complex numbers.

Use complex numbers in polynomial identities and equations.
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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