91影视

The age of an ancient seed can be calculated by using the following formula:

\(t = - \frac{{\ln (F)}}{k}\)

Where F is the fraction of carbon-14 remaining, k is the rate constant.

The age of seed 1 is calculated by using the above equation.

Given, the fraction (F) of carbon remaining for seed 1 is 0.7656, and k is 0.00012097. Substituting the values in the equation:

\(\begin{aligned}{l}t = - \frac{{\ln (F)}}{k}\\t = - \frac{{\ln (0.7656)}}{{0.00012097}}\\t = - \frac{{( - 0.2670)}}{{0.00012097}}\\t = 2207.9\\t = 2208\end{aligned}\)

Thus, the age of seed 1, which is not planted, is 2208 years old.

Given, F for seed 2 is 0.7752 and k is 0.00012097.

The age of seed 2 is calculated as:

\(\begin{aligned}{l}t = - \frac{{\ln (F)}}{k}\\t = - \frac{{\ln (0.7752)}}{{0.00012097}}\\t = - \frac{{( - 0.2546)}}{{0.00012097}}\\t = 2104.9\\t = 2105\end{aligned}\)

Thus, the age of seed 2, which is not planted, is 2105 years old.

Given, F for seed 3 is 0.7977, and k is 0.00012097.

The age of seed 3 is calculated as:

\(\begin{aligned}{l}t = - \frac{{\ln (F)}}{k}\\t = - \frac{{\ln (0.7977)}}{{0.00012097}}\\t = - \frac{{( - 0.2260)}}{{0.00012097}}\\t = 1868.4\\t = 1868\end{aligned}\)

Thus, the age of germinated seed 3 is 1868 years old.