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. How many grams of carbon-14 will be present in 5715 years?
A. Approximately 7 grams
B. Approximately 8 grams
C. Approximately 23 grams
D. Approximately 4 grams
My answer B
good answer
To find the number of grams of carbon-14 present in 5715 years, we need to substitute the value of t = 5715 into the decay model A = 16e^(-0.000121t).
Using a calculator, we can calculate A as follows:
A = 16e^(-0.000121 * 5715)
A ≈ 16 * e^(-0.69)
A ≈ 16 * 0.502
A ≈ 8.032
Therefore, approximately 8 grams of carbon-14 will be present in 5715 years.
So, your answer of option B is correct.
To find the amount of carbon-14 present in 5715 years, we need to plug in t = 5715 into the decay model A = 16e^(-0.000121t).
Let's perform the calculation step-by-step:
1. Plug in t = 5715 into the equation:
A = 16e^(-0.000121 * 5715)
2. Perform the exponential calculation:
A ≈ 16 * exp(-0.691215)
3. Use a calculator to evaluate the exponential function:
A ≈ 16 * 0.5 ≈ 8
Therefore, approximately 8 grams of carbon-14 will be present in 5715 years.
So your answer of B. Approximately 8 grams is correct.