An artifact originally had 16 grams of carbon- 14 present. The decay model $A=16 e^{-0.000121 t}$ describes the amount of carbon-14 present after $t$ years. Use the model to determine how many grams of carbon-14 will be present in 5710 years.
Answer
Final Answer: The amount of carbon-14 present after 5710 years will be approximately \(\boxed{8.02}\) grams.
Step 1 ：Given that the initial amount of carbon-14 present in the artifact is \(A_0 = 16\) grams, the decay constant is \(k = -0.000121\), and the time is \(t = 5710\) years.
Step 2 ：We are asked to find the amount of carbon-14 present after 5710 years. We can use the given decay model \(A = A_0 e^{kt}\) to calculate this.
Step 3 ：Substitute the given values into the decay model: \(A = 16 e^{-0.000121 \times 5710}\).
Step 4 ：Calculate the result to find the amount of carbon-14 present after 5710 years.
Step 5 ：Final Answer: The amount of carbon-14 present after 5710 years will be approximately \(\boxed{8.02}\) grams.
