Question

If an organism had 200 atoms of carbon-14 at death, how many atoms will be present after 14,325 years? Round the answer to the nearest hundredth.

Answer 1

Answer:

35.34 atoms will be present after 14,325 years.

Step-by-step explanation:

Given : Carbon-14 has a half-life of approximately 5,730 years. This exponential decay can be modeled with the function N(t) = N0. If an organism had 200 atoms of carbon-14 at death.

To find : How many atoms will be present after 14,325 years?

Solution :

The half-life exponential function modeled is $N=N_o(\frac{1}{2})^{\frac{t}{h}}$

Where, $N_o=200$ is the initial atoms

N is the total number of atoms.

t=14,325 years is the time  

h=5,730 years is the half-life time

Substitute the value in the formula,

$N=200(\frac{1}{2})^{\frac{14325}{5730}}$

$N=200(\frac{1}{2})^{2.5}$

$N=200(0.1767)$

$N=35.34$

Therefore, 35.34 atoms will be present after 14,325 years.