Q2ITD - Campbell Biology

Question

Using the equation you developed, the data from the table, and a calculator, estimate the ages of seed 1, seed 2, and seed 3.                

 

Seed Number	Fraction of Carbon-14 Remaining
Seed 1 (not planted)	0.7656
Seed 2 (not planted)	0.7752
Seed 3 (germinated)	0.7977

 

Step-by-Step Solution

Answer

The ages of the three seeds calculated are as follows:

 

• Seed 1: 2208 years old
• Seed 2: 2105 years old
• Seed 3: 1868 years old

Step 1: Equation for calculating age of a seed

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.

Step 2: Calculation of age of seed 1

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.

Step 3: Calculation of age of seed 2

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.

Step 4: Calculation of age of seed 3

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.