Asked by Victoria Cuevas on Mar 10, 2024

Verified

Radioactive carbon, $_{14}C$ , has a has a half-life of 5730 years. After 1000 years, 3.7 grams remain. What was the initial quantity of $_{14}C$ ? Round your answer to two decimal places.

A) 4.18 grams

B) 3.90 grams

C) 4.35 grams

D) 6.98 grams

E) 3.94 grams

A) 4.18 grams

B) 3.90 grams

C) 4.35 grams

D) 6.98 grams

E) 3.94 grams

Half-Life

Half-life is a term used in nuclear physics and chemistry to describe the time required for one half of the atoms of a radioactive substance to undergo decay.

- Apply the exponential model to solve real-world problems related to finance and physical sciences.
- Gain proficiency in the application of exponential growth and decay concepts in multiple contexts, encompassing population growth and the diminishment of radioactivity.

Verified Answer

LL

Lindsays LaFontaine

Mar 10, 2024

Final Answer :

A

Explanation :

The amount of radioactive carbon remaining after a certain period can be calculated using the formula $A=A_{0}(21 )_{Tt}$ , where $A$ is the amount remaining, $A_{0}$ is the initial amount, $t$ is the time elapsed, and $T$ is the half-life. Rearranging to solve for $A_{0}$ , we get $A_{0}=A(21 )_{−Tt}$ . Substituting $A=3.7$ grams, $t=1000$ years, and $T=5730$ years, we find $A_{0}≈4.18$ grams.

## Learning Objectives

- Apply the exponential model to solve real-world problems related to finance and physical sciences.
- Gain proficiency in the application of exponential growth and decay concepts in multiple contexts, encompassing population growth and the diminishment of radioactivity.