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 6990 years.
the amount of carbon-14 present in 6990 years will be approximately \boxed{} grams. (round to the nearest whole number)

Explanation:

Step1: Identify the formula and values

The decay model is \( A = 16e^{-0.000121t} \), and we need to find \( A \) when \( t = 6990 \).

Step2: Substitute \( t = 6990 \) into the formula

First, calculate the exponent: \( -0.000121\times6990 \approx -0.84579 \)
Then, calculate \( e^{-0.84579} \approx 0.429 \) (using a calculator for the exponential function)
Next, multiply by 16: \( A = 16\times0.429 \approx 6.864 \)

Step3: Round to the nearest whole number

Rounding 6.864 to the nearest whole number gives 7.

Answer:

7