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Darya [45]
3 years ago
12

The half-life of carbon-14, 14C, is approximately 5,730 years. A bone fragment is estimated to have originally contained 6 milli

grams of 14C. Write the exponential decay equation where A is the amount (in mg) of carbon-14 remaining in the bone fragment after t years.
Mathematics
1 answer:
anzhelika [568]3 years ago
6 0

Answer:

A(t)=6\cdot2^{-\frac{t}{5730 }

Step-by-step explanation:

The general formula for exponential decay given a half-life t_\frac{1}{2} is

N(t)=N_{0}\cdot2^{\frac{-t}{t_{1/2} }      

where N(t) is the amount at time t, N_0 is the initial amount (at time t=0), and t_\frac{1}{2} is the half life of the substance.

The half life of carbon-14, is approximately 5,730 years.

t_\frac{1}{2} = 5730 years

N_0= 6 milligrams

Therefore:

Amount of carbon-14 remaining in the bone fragment after t years is:

A(t)=6\cdot2^{-\frac{t}{5730 }

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