options: Prove and apply trigonometric identities.

Extend the domain of trigonometric functions using the unit circle.

Model periodic phenomena with trigonometric functions.

Build a function that models a relationship between two quantities.

Define, evaluate, and compare functions.

Construct and compare linear and exponential models and solve problems.

Understand the concept of a function and use function notation.

Use functions to model relationships between quantities.

Interpret expressions for functions in terms of the situation they model.

Interpret functions that arise in applications in terms of the context.

Build new functions from existing functions.

Analyze functions using different representations.
problem_activity: Task
A preserved plant is estimated to contain $1$ microgram (a millionth of a gram) of
Carbon $14$.    The amount of Carbon 14 present
in the preserved plant is modeled by the equation
$$
f(t) = A\left(\frac{1}{2}\right)^{\frac{t}{5730}}
$$
where $t$ denotes time since the death of the plant, measured in years,
and $A$ is the amount of Carbon $14$ present in the plant at death, measured
in micrograms.
How much Carbon $14$ was present in the living plant assuming it died  $5000$ years ago?
How much Carbon $14$ was present in the living plant assuming it
died $10000$ years ago?
The half-life of Carbon $14$ is the amount of time it takes for half of the
Carbon $14$ to decay.  What half-life does the expression for  the function $f$
imply for Carbon $14$?


correct_option_index: 8

11