options: Represent and model with vector quantities.

Use complex numbers in polynomial identities and equations.

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

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

Use properties of rational and irrational numbers.

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

Perform arithmetic operations with complex numbers.

Represent complex numbers and their operations on the complex plane.

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

Perform operations on matrices and use matrices in applications.

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

Reason quantitatively and use units to solve problems.

Perform operations on vectors.

Extend the properties of exponents to rational exponents.
problem_activity: Task
Carbon 14 is a form of carbon which decays exponentially over
time.
The amount
of Carbon 14 contained in a preserved plant is modeled
by the equation
$$
f(t) = 10\left(\frac{1}{2}\right)^{ct}.
$$
Time in this equation is measured in years
from the moment when the plant dies ($t = 0$) and the amount of Carbon 14 remaining in the preserved plant is measured in micrograms
(a microgram is one millionth of a gram).  The number $c$ in the exponential
measures the exponential rate of decay of Carbon $14$.
How many micrograms  of Carbon $14$ are in the plant at the time it died?
The best known estimate for the half-life of Carbon 14, that is the amount of time it takes for half of the
Carbon $14$ to decay, is $5730 \pm 40$ years.   Use this information to
calculate the range of possible values for the constant $c$ in the equation for $f$.
Use your answer from part (b) to find the range of years when there is
one microgram remaining in the preserved plant.


correct_option_index: 11