Question

solve the following using logarithmic or exponential Carbon-14 is an element used to find the approximate age of a wide array of objects. It has a half life of 5,730 years. Find the amount of Carbon-14 on a 100g sample after 20 years.

Answer 1

Answer:

$99.76\text{ g}$

Explanation:

Here, we want to calculate the amount of carbon-14 remaining

The formula to use here is as follows:

$N(t)=N_0(\frac{1}{2})^{\frac{t}{t_{_{_{half}}}_{}}}$

where:

N(t) is the mass left after some time or at a time t which is what we want to calculate

N_0 is the initial mass which is 100g in this case

t is the time which is 20 years

t_half is the half-life which is 5,730 years

Substituting these values, we have it that:

$\begin{gathered} N(t)\text{ = 100}\times0.5^{\frac{20}{5730}} \\ \\ N(t)\text{ = 99.76 g} \end{gathered}$