Question

an artifact originally had 16 grams of carbon - 14 present. the decay model a = 16e^(-0.000121t) 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 8191 years.
the amount of carbon - 14 present in 8191 years will be approximately grams.
(round to the nearest whole number.)

Explanation:

Step1: Substitute t value

We are given the decay model $A = 16e^{-0.000121t}$ and $t = 8191$. Substitute $t = 8191$ into the formula: $A=16e^{- 0.000121\times8191}$.

Step2: Calculate the exponent

First, calculate $-0.000121\times8191=-0.991111$. Then our formula becomes $A = 16e^{-0.991111}$.

Step3: Calculate the exponential part

We know that $e^{-0.991111}\approx0.3715$.

Step4: Calculate the final amount

Multiply 16 by $0.3715$: $A = 16\times0.3715 = 5.944$.

Answer:

6