By comparing the amount of carbon-14 to amount of carbon-12, one can determine approx how long ago the organism died.
The half-life of carbon-14 is 5730 years. Assume the initial quantity of carbon-14 is 600 milligrams.
the equation is
A (t)=600*(.5)^(t)
(0,600)
(1,300)
(2,150)
(3,75)
(4,37.5)
(5,18.75)
(6,9.375)
(7,4.6875)
from the table, estimate how many milligrams are left after 40,000 years. Round answer to 2 decimal places.
I'VE TRIED PLUGGING IT TO THR FORMULA, BUT IT GIVES ME A WRONG ANSWER. HELP!!
No, your equation cuts the amount in half every time t increases by 1.
Since the half-life is 5730 years, you want the amount to be cut by half only that often. So,
A9t) = 600(0.5)^(t/5730)
To do a sanity check on your answer, note that 40000 years is about 7 half-lives, so expect the amount to be about 1/128 of the original 600 mg, or about 4.6mg.
To estimate how many milligrams of carbon-14 are left after 40,000 years using the formula A(t) = 600 * (0.5)^(t/5730), you need to calculate the value of A(40,000/5730). It seems like you may have made an error when plugging it into the formula. Let's correct it together step by step:
1. Start by substituting t = 40,000 into the formula:
A(40,000) = 600 * (0.5)^(40,000/5730)
2. Now, divide 40,000 by 5730:
t/5730 = 40,000 / 5730 ≈ 6.98
3. Substitute the value of t/5730 into the formula:
A(40,000) = 600 * (0.5)^(6.98)
4. Calculate (0.5)^(6.98) using a calculator:
(0.5)^(6.98) ≈ 0.0214
5. Finally, calculate A(40,000):
A(40,000) = 600 * 0.0214 ≈ 12.84
Therefore, approximately 12.84 milligrams of carbon-14 are estimated to be left after 40,000 years.