# The half-life of carbon-14 is about 5370 years. What percent of the original carbon-14 would you expect to find in a sample after 2500 years?

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The half life of carbon-14 = 5370 years.

Let m be the mass of the carbon-14, now

Therefore, the mass ofl carbon-14 to be left out after t tears = m(1/2)^ (t/5370), put t= 2500

= m*(1/2)^(2500/5370)

=0.724195266m

=72.4195266% is the remaining carbon-14, after 2500 yrs

If t is the half life of a radioactive substance the percentage (p) of the radioactive material left after time T is given by:

p = 100*[0.5^(T/t)]

It is given:

Half life of carbon-14 = t = 5370 years, and

Actual time elapsed = T = 2500 years

Substituting these values in equation for p we get:

p = 100*[0.5^(2500/5370)] = 72.4195

Answer:

72.4195 percent of carbon-14 will remain after 2500 years