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 8849 years. the amount of carbon - 14 present in 8849 years will be approximately (square) grams (round to the nearest whole number.)

Explanation:

Step1: Substitute the value of \(t\) into the formula

Given the formula \(A = 16e^{-0.000121t}\), and \(t = 8849\). Substitute \(t\) into the formula: \(A=16e^{-0.000121\times8849}\).

Step2: Calculate the exponent

First, calculate \(- 0.000121\times8849=-1.070729\).

Step3: Calculate the value of \(e^{-1.070729}\)

We know that \(y = e^{x}\), and using a calculator, \(e^{-1.070729}\approx0.3436\).

Step4: Calculate the value of \(A\)

Multiply \(16\) by \(0.3436\): \(A = 16\times0.3436 = 5.4976\).

Answer:

\(5\)