standard_description: Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., p^(2)). For example, by truncating the decimal expansion of Ö2, show that Ö2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.
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 $14$?


aligns: no