Question

The half-life of carbon-14, 14C, is approximately 5,730 years. A bone fragment is estimated to have originally contained 6 milligrams of 14C. Write the exponential decay equation where A is the amount (in mg) of carbon-14 remaining in the bone fragment after t years.

Answer 1

Answer:

$A(t)=6\cdot2^{-\frac{t}{5730 }$

Step-by-step explanation:

The general formula for exponential decay given a half-life $t_\frac{1}{2}$ is

$N(t)=N_{0}\cdot2^{\frac{-t}{t_{1/2} }$      

where N(t) is the amount at time t, $N_0$ is the initial amount (at time t=0), and $t_\frac{1}{2}$ is the half life of the substance.

The half life of carbon-14, is approximately 5,730 years.

$t_\frac{1}{2}$ = 5730 years

$N_0$= 6 milligrams

Therefore:

Amount of carbon-14 remaining in the bone fragment after t years is:

$A(t)=6\cdot2^{-\frac{t}{5730 }$