Question

an old bone contains 80% of its original carbon - 14. use the half - life model to find the age of the bone. find an equation equivalent to $p(t)=a\left(\frac{1}{2}\
ight)^{\frac{t}{5730}}$\
options:\
a. $p(t)=a\left(\frac{1}{2}\
ight)^{\frac{t}{5730}}$ (marked with x)\
5.730 $\cdot p(t)=a\left(\frac{1}{2}\
ight)^t$\
$\frac{p(t)}{a}=\left(\frac{1}{2}\
ight)^{\frac{t}{5730}}$ (marked with check and complete)\
find the value of $\frac{p(t)}{a}$ for this problem.\
$\frac{p(t)}{a}=\square$ (with done button)

Explanation:

Step1: Understand the Problem

The problem is about carbon - 14 dating. The bone contains 80% of its original carbon - 14. We need to find the value of \(\frac{P(t)}{A}\), where \(P(t)\) is the current amount of carbon - 14 and \(A\) is the original amount.

Step2: Determine the Ratio

If the bone contains 80% of its original carbon - 14, then the ratio of the current amount (\(P(t)\)) to the original amount (\(A\)) is \(0.8\) or \(\frac{80}{100}=\frac{4}{5} = 0.8\).

Answer:

\(0.8\) (or \(\frac{4}{5}\))